Question 13 Marks
How many persons can be accommodated in a hall of length $16\ m$. Breadth $12.5\ m$ and height $4.5\ m$, assuming that $3.6m^3$ of air is required for each person?
AnswerLength of hall $(l) = 16\ m$
Breadth $(b) = 12.5\ m$
Height $(h) = 4.5\ m$
Volume of air in it $= l \times b \times h$
$= 16 \times 12.5 \times 4.5m^3$
$= 900m^3$
Air for one person is required $= 3.6m^3$
Number of person which can be accommodated in the hall $=\frac{900}{3.6}$
$=\frac{900\times10}{36}$
$=250$
View full question & answer→Question 23 Marks
A particular brand of talcum powder is available in two packs, a plastic can with a square base of side $5\ cm$ and of height $14\ cm$, or one with a circular base of radius $3.5\ cm$ and of height $12\ cm$. Which of them has greater capacity and by how much?
AnswerIn frist case,
Side of square base $(a) = 5\ cm$.
And height $(h) = 14\ cm$.
Volume $= 5 \times 5 \times 14 = 350cm^3$
In second case,
Radius of the circular base $(r) = 3.5\ cm$.
Height $(h) = 12\ cm$.
Volume $\pi\text{r}^2\text{h}$
$=\frac{22}{7}\times3.5×3.5×12\text{cm}^3$
$=462\text{cm}^2$
Hence second type of circular plastic can has greater capacity.
Difference $= 462 - 350$
$= 112\ cm^3$.
View full question & answer→Question 33 Marks
The curved surface area of a cylindrical pillar is $264m^2$ and its volume is $924m^3$. Find the diameter and height of the pillar.
AnswerCurved surface area $=2\pi\text{rh}=264\text{m}^2$
$\therefore\text{r}=\frac{264}{2\pi\text{h}}=\frac{132}{\pi\text{h}}\text{m}$
Volume $=\pi\text{r}^2\text{h}=\pi\times\frac{132}{\pi\text{h}}\times\frac{132}{\pi\text{h}}\times\text{h}=924\text{m}^3$
$\therefore\text{h}=-\frac{132\times132\times7}{22\times924}=6\text{m}$
Now, $\text{r}=\frac{132}{\pi\text{h}}=\frac{13 2\times7}{22\times6}=7\text{m}$
i.e., deameter of the piller, $d = 7 \times 2 = 14\ m$.
View full question & answer→Question 43 Marks
A swimming pool is $260\ m$ long and $140\ m$ wide. If $54600$ cubic metres of water is pumped into it, find the height of the water level in it.
AnswerLength of pool $= 260\ m,$
and width $= 140\ m.$
Volume of water $= 54600m^3$
$\therefore$ Height of water $=\frac{\text{Volume}}{\text {Length}\times\text{breadth}}$
$=\frac{546000}{260\times140}\text{m}$
$=\frac{3}{2}=1.5\text{m}$
View full question & answer→Question 53 Marks
How many bricks, each of size $25\ cm \times 13.5\ cm \times 6\ cm$, will be required to build a wall $8\ m$ long, $5.4\ m$ high and $33\ cm$ thick?
AnswerLength of wall $(l) = 8m = 800\ cm$
Height $(h) = 5.4m = 540\ cm$
Width $(b) = 33\ cm$
$\therefore$ Volume of wall $= l \times b \times h,$
$= 800 \times 540 \times 33cm^3$
Volume of one brick $= 25 \times 13.5 \times 6\ cm^3$
$= 2025\ cm^3$
$\therefore$ No. of bricks $=\frac{14256000}{2025}=7040$
View full question & answer→Question 63 Marks
The rainfall recorded on a certain day was $5\ cm$. Find the volume of water that fell on a $2$-hectare field.
AnswerArea of field $= 2$ hectare,
$= 20000\ m^2$
Rainfall $= 5\ cm. = 005\ m$
Volume of water of rainfall,
= Area of field $\times $ height of rainfall water,
$= 20000 \times 0.05m^3$
$= 1000m^3$
View full question & answer→Question 73 Marks
Find the cost of painting $15$ cylindrical pillars of a building at $Rs.\ 2.50$ per square metre if the diameter and height of each pillar are $48\ cm$ and $7$ metres respectively.
AnswerDiameter of a cylindrical pillar $= 48\ cm$.
Radius $(r)$ $=\frac{48}{2}=24\text{cm}.$ $\frac{24}{100}\text{m}$
Height $(h) = 7\ m$
$\therefore$ Lateral surface area of one pillar $=2\pi\text{rh}=2\times\frac{22}{7}\times\frac{24}{100}\times7\text{m}^2$
$=\frac{1056}{100}\text{m}^2$
Surface area of $15$ pillars $=\frac{1056}{100}\times15\text{m}^2=\frac{15840}{100}\text{m}^2$
Rate of painting $= Rs.$ $2.50$ per sq. m.
$\therefore$ Total cost $=\text{Rs.}2.50\times\frac{15840}{100}$
$=\text{Rs}.396$
View full question & answer→Question 83 Marks
A box with a lid is made of wood which is $3\ cm$ thick. Its external length, breadth and height are $56\ cm, 39\ cm$ and $30\ cm$ respectively. Find the capacity of the box. Also find the volume of wood used to make the box.
AnswerOuter length of the box $= 56\ cm$
Width $= 39\ cm$
And height $= 30\ cm$
Volume $= 56 \times 39 \times 30$
$= 65520\ cm^3$
Thickness of wood used $= 3\ cm.$
$\therefore$ Inner length $= 56 - 2 \times 3$
$= 56 - 6$
$= 50cm$
Width $= 39 - 2 \times 3$
$= 39 - 6$
$= 33\ cm$
And height $ = 30 - 2 \times 3$
$= 30 - 6$
$= 24\ cm$
$\therefore$ Inner volume of the box $= 50 \times 33 \times 24cm^3$
$= 39600\ cm^3$
And volume of wood used = Outer volume - Inner volume
$= (65520 - 39600)cm^3$
$= 25920\ cm^3$
View full question & answer→Question 93 Marks
The dimensions of a rectangular water tank are $2\ m$ $75\ cm$ by $1\ m$ $80\ cm$ by $1\ m$ $40\ cm$. How many litres of water does it hold when filled to the brim?
AnswerLength of water tank $(l) = 2\ m$
$75\ cm = 2.75\ m$
Breadth $(b) = 1\ m 80\ cm$
$= 1.80\ m,$ and
height $(h) = 1\ m 40\ cm$
$= 1.40\ m$
Volu\ me of water filled in it $= l.b.h$
$= 2.75 \times 1.80 \times 1.40\ m^3$
$= 6. 93\ m^3$
Water in litres $= 6.93 \times 1000$
$= 6930$ litres $(1\ m^3= 1000$ litres$)$
View full question & answer→Question 103 Marks
Find the number of coins, $1.5\ cm$ in diameter and $0.2\ cm$ thick, to be melted to form a right circular cylinder with a height of 10cm and a diameter of $4.5\ cm$.
AnswerVolume of the coin $=\pi\text{r}^2\text{h}=\frac{22}{7}\times0.75\times0.75\times0.2$
Volume of the cylinder $=\pi\text{r}^2\text{h}=\frac{22}{7}\times2.25\times2.25\times10$
No. of coins $=\frac{\text{Volume of cylinder}}{\text{Volume of coin}}$
$=\frac{2.25\times2.25\times10}{0.75\times0.75\times0.2}=450\text{ coins}$
$\therefore$ $450$ coins must be melted to form the required cylinder.
View full question & answer→Question 113 Marks
The circumference of the base of a cylinder is $88\ cm$ and its height is $60\ cm$. Find the volume of the cylinder and its curved surface area.
AnswerCircumference of the base of cylinder $= 88\ cm$.
$\because\text{radius}=\frac{\text{Circumference}}{2\pi}=\frac{88\times7}{2\times22}=14\text{cm}$
Height $(h) = 60\ cm$.
$\therefore\text{Volume}=\pi\text{r}^2\text{h}=\frac{22}{7}\times14\times14\times60\text{cm}^3$
$=36960\text{cm}^3$
And curved surface area $=2\pi\text{rh}$
$= 88 \times 60 = 5280\ cm^2$
View full question & answer→Question 123 Marks
The lateral surface area of a cylinder of length $14\ m$ is $220m^2$. Find the volume of the cylinder.
AnswerLateral surface of cylinder $= 220m^2$
Height $(h) = 14\ m$
Let radius of a cylinder $= r$
Then $2\pi\text{rh}=220$
$\Rightarrow2\times\frac{22}{7}\times\text{r}\times14=220$
$\Rightarrow\text{r}=\frac{220\times7}{2\times22\times14}=\frac{5}{2}=2.5\text{m}$
$\therefore\text{Volume}=\pi\text{r}^2\text{h}$
$=\frac{22}{7}\times(2.5)^2\times14\text{m}^3$
$=\frac{22}{7}\times2.5\times2.5\times14\text{m}^3$
$=22\times6.25\times2=275\text{m}^3$
View full question & answer→Question 133 Marks
If the length of each edge of a cube is doubled, how many times does its volume become? How many times does its surface area become?
AnswerLet edge of given cube $= a$ Volume $= a^3$
And surface area $= 6a^2$
By doubing the edge of cube $3$ the side of new cube $= a \times 2 = 2a$
Volume $(2a)^3= 8a^3$
And surface area $= 6(2a)^2= 6 × 4a^2= 24a^2= 4 × 6a^2$
It is clear from the above that,
Volume is increased $8$ times and surface area is $4$ times.
View full question & answer→Question 143 Marks
A rectangular vessel $22\ cm$ by $16\ cm$ by $14\ cm$ is full of water. If the total water is poured into an empty cylindrical vessel of radius $8\ cm$, find the height of water in the cylindrical vessel.
AnswerLength of rectangular vessel $(l) = 22\ cm.$
Breadth $(A) = 16\ cm.$
And height $(A) = 14\ cm.$
$\therefore$ Volume of vessel $= lbh$
$=22 \times 16 \times 14 \mathrm{~\ cm}^3=4928 \mathrm{~\ cm}^3$
Volume of water in the cylindrical vessel $= 4928\ cm^3$
Radius $(r) = 8\ cm.$
Let height of water in the vessel $= h$
$\therefore\pi\text{r}^2\text{h}=4928$
$\Rightarrow\frac{22}{7}\times8\times8\times\text{h}=4928$
$\Rightarrow\text{h}=\frac{4928\times7}{22\times8\times8}\Rightarrow\text{h}=24.5$
Hence height of water $= 24.5\ cm.$
View full question & answer→Question 153 Marks
Find the volume, lateral surface area and the total surface area of a cube whose edges measures: $5.6\ cm$.
AnswerEdge of cube $(a) = 5.6\ cm.$
$a.$ Volume $\mathrm{a}^3=(5.6)^3 \mathrm{~cm}^3$
$=5.6 \times 5.6 \times 5.6 \mathrm{~cm}^2=175.616 \mathrm{~cm}^3$
$b.$ Lateral surface area $=4 \mathrm{a}^2$
$=4(5.6)^2=4 \times 5.6 \times 5.6 \mathrm{~cm}^2$
$=125.44 \mathrm{~cm}^2$
$c.$ Total surface area $=6 \mathrm{a}^2=6 \times(5.6)^2 \mathrm{~cm}^2$
$=6 \times 5.6 \times 5.6 \mathrm{~cm}^2=188.16 \mathrm{~cm}^2$
View full question & answer→Question 163 Marks
A pit $5\ m$ long and $3.5\ m$ wide is dug to a certain depth. If the volume of earth taken out of it is $14\ m^3$, what is the depth of the pit?
AnswerLength of pit $(l) = 5\ m$
Width $(b) = 3.5\ m$
Let depth of pit $= h$
Then volume of earth dug out,
$= l.b.h = 5 \times 3.5 \times h = 17.5h m^3$
But volume of earth $= 14m^3$
$17.5h = 14$
$\text{h}=\frac{14}{17.5}=\frac{140}{175}$
$\Rightarrow\text{h}=\frac{4}{5}\text{m}$
$=\frac{4}{5}\times100$
$=80\text{cm.}$
View full question & answer→Question 173 Marks
The dimensions of a metal block are $2.25\ m$ by $1.5\ m$ by $27\ cm$. It is melted and recast into cubes, each of side $45\ cm$. How many cubes are formed?
AnswerLength of metal block $(l) = 2.25\ m = 225\ cm$
Width $(b) = 1.5m = 150\ cm$
And height $(h) = 27\ cm$
Volume of block $= l \times b \times n$
$= 225 \times 150 \times 27cm^2$
$= 911250cm^3$
Side of each cube $= 45\ cm.$
Volume of each cube $= a^2$
$= 45 \times 45 \times 45$
$= 94125\ cm^3$
Number of cubes $=\frac{911250}{91125}$
$= 10.$
View full question & answer→Question 183 Marks
Find the volume, lateral surface area and the total surface area of a cube whose edges measures: $7\ m$.
Answer
Edge of cube $(a) = 7\ m$
$a.$ Volume $=a^3=(7)^3$
$=7 \times 7 \times 7 \mathrm{~m}^3$
$=343 \mathrm{~m}^3$
$b.$ Leteral surface area $=4 a^2$
$=4(7)^2=4 \times 49 \mathrm{~m}^2=196 \mathrm{~m}^2$
$c.$ Total surface area $=6 a^2=6(7)^2 m^2$
$=6 \times 49=294 \mathrm{~m}^2$ View full question & answer→Question 193 Marks
Find the volume of a cube whose total surface area is $384cm^2$.
AnswerTotal surface area $= 6a^2$
$\Rightarrow6\text{a}^2=384$
$\Rightarrow\text{a}=\sqrt{\frac{384}{6}}=8\text{cm}$
$\therefore$ Volume $=\text{a}^2=512\text{cm}^3$
View full question & answer→Question 203 Marks
The size of a matchbox is $4\ cm \times 2.5\ cm \times 1.5\ cm$. What is the volume of a packet containing $144$ matchboxes? How many such packets can be placed in a carton of size 1$.5\ m \times 84\ cm \times 60\ cm$?
AnswerVolume of one matchbox $= 4 \times 2.5 \times 1.5\ cm^3= 15\ cm^3$
Volume of 144 matchbox $= 15 \times 144\ cm^3$
or volume of one packet $= 2160\ cm^3$
Length of catron $(l) = 1.5\ m = 150\ cm.$
Breadth $(b) = 84\ cm.$
Volume of one carton $= l \times b \times h,$
$= 1502 \times 84 \times 60cm^3$
$= 756000\ cm^3$
No. of packets $=\frac{756000}{2160}$
$= 350$
View full question & answer→Question 213 Marks
The area of a courtyard is $3750m^2$. Find the cost of covering it with gravel to a height of $1\ cm$ if the gravel costs $Rs.\ 6.40$ per cubic metre.
AnswerArea of courtyard $= 3750m^2$
Height of gravel $= 1\ cm.$
Volume of gravel $=3750\times\frac{1}{100}\text{m}^3$
$= 37.50m^3$
Cost of $1m^3$ gravel $= Rs. 6.40$
Total cost $= Rs. 6.40 \times 37.50$
$= Rs. 240$
View full question & answer→Question 223 Marks
A box with a lid is made of wood which is $3\ cm$ thick. Its external length, breadth and height are $56\ cm, 39\ cm$ and $30\ cm$ respectively. Find the capacity of the box. Also find the volume of wood used to make the box.
AnswerOuter length of the box $= 56\ cm$
Width $= 39\ cm$
And height $= 30\ cm$
Volume $= 56 \times 39 \times 30$
$= 65520\ cm^3$
Thickness of wood used $= 3\ cm.$
$\therefore$ Inner length $= 56 - 2 \times 3$
$= 56 - 6$
$= 50\ cm$
Width $= 39 - 2 \times 3$
$= 39 - 6$
$= 33\ cm$
And height $= 30 - 2 \times 3$
$= 30 - 6$
$= 24\ cm$
$\therefore$ Inner volume of the box $= 50 \times 33 \times 24\ cm^3$
$= 39600\ cm^3$
And volume of wood used = Outer volume - Inner volume
$= (65520 - 39600)\ cm^3$
$= 25920\ cm^3$
View full question & answer→Question 233 Marks
Find the volume, lateral surface area and the total surface area of a cube whose edges measures: $8\ dm, 5\ cm.$
AnswerEdge of cube $(a) = 8\ dm\ 5\ cm = 85\ cm$.
$a.$ Volume $=a^3=(85)^3 \mathrm{~\ cm}^3$
$=85 \times 85 \times 85=614125 \mathrm{~\ cm}^3$
$b.$ Lateral surface area $=4 \mathrm{a}^2$
$=4 \times(85)^2 \mathrm{~\ cm}^2$
$=4 \times 85 \times 85=28900 \mathrm{~\ cm}^2$
$c.$ Total surface area $=6 \mathrm{a}^2=6(85)^2 \mathrm{~\ cm}^2$
$=6 \times 85 \times 85=43350 \mathrm{~\ cm}^2$
View full question & answer→Question 243 Marks
The volume of a circular iron rod of length $1\ m$ is $3850cm^3$. Find its diameter.
AnswerVolume of cylindrical rod $= 3850cm^3$
Length of rod $(h) = 1m = 100cm$
Let radius of the base of the rod $= r$
Then volume $=\pi\text{r}^2\text{h}$
$\therefore\pi\text{r}^2\text{h}=3850$
$\Rightarrow\frac{22}{7}\times\text{r}^2\times100=3850$
$\Rightarrow\text{r}^2=\frac{3850\times7}{2200}=\frac{1225}{100}=\Big(\frac{35}{10}\Big)^2$
$=(3.5)^2$
$\therefore\text{r}=3.5\text{m}$
Hence diameter $= 2r = 2 × 3.5 $
$= 7cm.$
View full question & answer→Question 253 Marks
A closed cylindrical tank of diameter $14\ m$ and height $5\ m$ is made from a sheet of metal. How much sheet of metal will be required?
AnswerDeameter of close cylinder $= 14\ m$
Radius $=\frac{14}{2}$ $= 7\ m$
Height $= 5$
$\therefore$ Total surface area of closed cylinder, $=2\pi\text{rh}+2\pi\text{r}^2$
$=2\pi\text{r}(\text{h}+\text{r})$
$=2\times\frac{22}{7}\times7\times(5+7)\text{m}^2$
$=44\times12=528\text{m}^2$
View full question & answer→Question 263 Marks
Find the height of the cylinder whose volume is $1.54\ m^3$ and diameter of the base is $140\ cm$?
AnswerVolume of cylinder $= 1.54m^3$
$= 1540000cm^3$
Diameter of its base $= 140\ cm$
Radius $(r) = 70\ cm$
$\therefore\text{Height}=\frac{\text{Volume}}{\pi\text{r}^2}=\frac{1540000\times7}{22\times70\times70}\text{cm}$
$=100\text{cm}=1\text{m}$
View full question & answer→Question 273 Marks
A solid rectangular piece of iron measures $1.05\ m \times 70\ cm \times 1.5\ cm$. Find the weight of this piece in kilograms if $1cm^3$ of iron weighs $8$ grams.
AnswerLength of iron $(l) = 1.05\ m = 105\ cm,$
Breadth $(b) = 70\ cm$ and height $(h) = 1.5\ cm.$
Volume of iron $= l \times b \times h = 105 \times 70 \times 1.5cm^3$
$= 11025cm^3$ Weight of $1cm^3$ iron $= 8 gram.$
Total weight $= 11025 \times g = 88200g$
$=\frac{88200}{1000}\text{kg}$
$88.2\text{kg.}$
View full question & answer→Question 283 Marks
A road roller takes $750$ complete revolutions to move once over to level a road. Find the area of the road if the diameter of the road roller is $84\ cm$ and its length is $1\ m$.
AnswerNo. of revolutions $= 750$
Diameter of road roller $= 84\ cm$
Length $(h) = 1\ m$
Radius $=\frac{84}{2}=42\text{cm}=0.42\text{m}$
$\therefore$ Surface area $=2\pi\text{rh}$
$=2\times\frac{22}{7}\times\frac{42}{100}\times1\text{m}^2$
$=\frac{264}{100}\text{m}^2$
$\therefore$ Area of road $=\frac{264}{100}\times750\text{m}^2$
$=1980\text{m}^2$
View full question & answer→Question 293 Marks
The surface area of a cube is $1176cm^2$. Find its volume.
AnswerSurface area of a cube $= 1126cm^2$
Let edge of the cube $= a$
Then $6a^2= 1176 ⇒ a^2=\frac{1176}{6}=196$
$⇒ a^2= (14)^2⇒ a = 14cm.$
$\therefore$ Volume of cube $= a^3= (14)^3cm^3$
$= 14 × 14 × 14cm^3= 2744cm^3$
View full question & answer→Question 303 Marks
The volume of a block of gold is $0.5m^3$. If it is hammered into a sheet to cover an area of $1$ hectare, find the thickness of the sheet.
Answer$ =0.5 \mathrm{~m}^3$
$ =0.5 \times 1000000 \mathrm{~cm}^3 $
$ =500000 \mathrm{~cm}^3 $
$ \text { Area of sheet formed }=1 \text { heckare } $
$ =10000 \mathrm{~m}^2=10000 \times 10000 \mathrm{~cm}^2 $
$\therefore$ Thickness of sheet $=\frac{500000}{10000\times10000}\text{cm}$
$=\frac{5}{1000}\text{cm}=\frac{5}{1000}\times10$
$=\frac{5}{1000}\text{mm}=0.05\text{mm}$
View full question & answer→Question 313 Marks
The volume of a room is $378m^3$ and the area of its floor is $84m^2$. Find the height of the room.
AnswerVolume of a room $= 378m^3$
Area of its floor $= 84m^2$
Height $=\frac{\text{Volume}}{\text{Area}}$
$=\frac{378}{84}\text{m}$
$=4.5\text{m}$
View full question & answer→Question 323 Marks
A cardboard box is $1.2\ m$ long, $72\ cm$ wide and $54\ cm$ high. How many bars of soap can be put into it if each bar measures 6cm × 4.5cm × 4cm?
AnswerLength of cardboard box $(l)$,
$= 1.2\ m = 120\ cm.$
Breadth $(b) = 72\ cm.$
Height $(h) = 54\ cm.$
Volume of box $= l \times b \times h$
$= 120 \times 72 \times 54\ cm^3$
$= 466560\ cm^3$
Volume of one soap bar $= 6 \times 4.5 \times 4\ cm^3$
$= 108\ cm^3$
No, of bars to be kept in it $=\frac{466560}{108}$
$= 4320$
View full question & answer→Question 333 Marks
A solid cubical block of fine wood costs $Rs. 256$ at $Rs. 500$ per $m^2$. Find its volume and the length of each side.
AnswerTotal cost of wood $= Rs. 256$
Rate $= Rs. 500$ per $m^3$
Volume od wood $=\frac{256}{500}=0.512\text{m}^3$
$= 0.512 \times 100 \times 100 \times 100cm^3$
$= 512000cm^3$
Let length of each side $= a$
Then $a^3= 512000 = (80)^3$
$a = 80$
Hence length of each side $= 80cm.$
View full question & answer→Question 343 Marks
The radius and height of a cylinder are in the ratio $5 : 7$ and its volume is $550cm^2$. Find its radius and height.
Answer$\frac{\text {Radius}}{\text{Height}}=\frac{\text{r}}{\text{h}}=\frac{5}{7}$
$\Rightarrow\text{r}=\frac{5}{7}\text{h}$
Now, volume $=\pi\text{r}^2\text{h}=\frac{22}{7}\times\frac{5}{7}\text{h}\times\text{h}=550\text{cm}^3$
$\therefore\text{h}=\sqrt[3]{\frac{550\times7\times7\times7}{22\times5\times5}}=7\text{cm}$
Also, $\text{r}=\frac{5}{7}\text{h}=5\text{cm}$
View full question & answer→Question 353 Marks
A river $2m$ deep and $45m$ wide is flowing at the rate of $3km/ h$. Find the quantity of water that runs into the sea per minute.
AnswerSpeed of water $= 3km/ h$
Length of water flow in $1$ minute
$=\frac{ 3\text{km}}{60\text {m}}$
$=\frac{3000}{60}$
$=50\text{m}$
Width of river $= 45m$
Depth of river $= 2m$
Volume of water in $1$ minute
$= 45 \times 2 \times 50m^3$
$= 4500m^3$
View full question & answer→Question 363 Marks
The volume of a cube is $729cm^3$. Find its surface area.
AnswerVolume of a cube $=729 \mathrm{~cm}^3$
$ \text { Let edge of cube }=(9)^3 $
$\mathrm{a}=9 \mathrm{~cm}$
$ \text {. Hence surface }=6 \mathrm{a}^2=6(9)^2 \mathrm{~cm}^2$
$=6 \times 81$
$=486 \mathrm{~cm}^2$
View full question & answer→Question 373 Marks
A rectangular water tank is $90\ cm$ wide and $40\ cm$ deep. If it can contain $576$ litres of water, what is its length?
AnswerWidth of tank $= 90\ cm$ $=\frac {90}{100} \text{m}$
Depth $= 40\ cm$ $=\frac{40}{100}\text{m}$
Water $= 576$ liter,
$\therefore$ Volume of tank $=\frac{576}{100}\text{cm}^3$
$\therefore$ Length $=\frac{\text{Volume}}{\text{Width}\times\text{Depth}}$
$=\frac{576\times100\times100}{90\times40\times1000}$
$=\frac{16}{10}\text{m}=1.6\text{m}$
View full question & answer→Question 383 Marks
A beam of wood is $5\ m$ long and $36\ cm$ thick. It is made of $1.35\ m^3$ of wood. What is the width of the beam?
AnswerVolume of wood $= 1.35\ m^3$
Length of beam $= 5\ m$
Thickness $= 36\ cm$ $=\frac{36}{100}\text{m}.$
$\text{Width}=\frac{\text{Volume}}{\text{Length}\times\text{thickness}}$
$=\frac{1.35\times100}{5\times36}=\frac{135\times100}{100\times5\times36}$
$=\frac{3}{4}\text{m}=0.75\text{m}$
$=75\text{cm}$
View full question & answer→