Question 13 Marks
A marble tile measures $12\ cm \times 10\ cm$. How many tiles will be required to cover a wall of size $4m$ by $3m$? Also, find the total cost of the tiles at $Rs. 22.50$ per tile.
AnswerHere, length of the marble tile $= 12\ cm$
And, breadth of the marble tile $= 10\ cm$
$\therefore$ Area of the marble tile $= (12 \times 10)$
$= 120\ cm^2$
Now, length of the wall $= 4m$
$= 400\ cm$
Breadth of the wall $= 3m$
$= 300\ cm$
$\therefore$ Area of the marble tile $= (12 \times 10)$
$= 120\ cm^2$
Now, length of the wall $= 4m = 400\ cm$
Breadth of the wall $= 3m$
$= 300\ cm$
$\therefore$ Area of the wall $= (400 \times 300)$
$= 120000\ cm^2$
Hence,number of the marble tile $=\frac{120000}{120}$
$= 1000$
Now, rate of the tile $= Rs. 22.50$ per tile
$\therefore$ Total cost of tiles $= Rs. 1000 \times 22.50$
$= Rs. 22500$
View full question & answer→Question 23 Marks
The length and breadth of a rectangular field are in the ratio $5 : 4.$ If its perimeter is $108m$, find the dimensions of the field.
View full question & answer→Question 33 Marks
Find the area of a square whose diagonal is $5\sqrt{2}\text{cm}.$ Hint: Area $=\Big[\frac{1}{2}\times (\text{diagonal})^2\Big]\text{sq}-\text{units}.$
AnswerArea of the square $=\Big\{\frac{1}{2}\times(\text{Diagonal})^2\Big\}\text{sq}-\text{units}$
$=\Big\{\frac{1}{2}\times (5\sqrt{2})^2\Big\}\text{cm}^2$
$=\Big\{\frac{1}{2}\times (5)^2\times (\sqrt{2})^2\Big\}\text{cm}^2$
$=\Big\{\frac{1}{2}\times25\times2\Big\}\text{cm}^2$
$=\Big(\frac{1}{2}\times 50\Big)\text{cm}^2$
$=25\text{cm}^2$
View full question & answer→Question 43 Marks
Find the area of a square whose perimeter is $84\ cm.$
AnswerLet one side of the square be $x \ cm.$
Perimeter of the square $= (4 \times $ side)
$=(4 \times x)cm$
$4x \ cm$
It is given that the perimeter of the square is $84\ cm.$
$\Rightarrow 4\text{x}=84$
$\Rightarrow \text{x}=\frac{84}{4}$
$=21$
Thus, one side of the square is $21\ cm.$
Area of the square $= (Side)^2$
$ = (21)^2\ cm^2$
$= 441\ cm^2$
View full question & answer→Question 53 Marks
The cost of putting a fence around a square field at $Rs. 35$ per metre is $Rs. 4480$. Find the length of each side of the field.
AnswerTotal cost of fencing a square field $= Rs. 4480$
Rate of fencing $= Rs. 35$ per $m$
$\therefore$ Perimeter of square field $=\frac{\text{Total cost}}{\text{Rate}}$
$=\frac{4480}{35}$
$=128\text{m}$
$\therefore$ Side of the square $=\frac{\text{Perimeter}}{4}$
$=\frac{128}{4}$
$=32\text{m}$
Hence, the length of each side of the field is $32m.$
View full question & answer→Question 63 Marks
The cost of cultivating a rectangular field at $Rs. 35$ per square meter is $Rs. 71400.$ If the width of the field is $40m$, find its length. Also, find the cost of fencing the field at $Rs 50$ per meter.
AnswerTotal cost of cultivating $= Rs. 71400$
Rate of cultivating = Rs. $35/ m^2$
Area of the field $=\frac{71400}{35}$
$= 2040m^2$
Width of the field $= 40m$
So, the length of the field $=\frac{2040}{40}$
$= 51m$
Hence, the length of the field is $51m.$
$\therefore$ Perimeter of the field $= 2(51 + 40) = 182m$
$\therefore$ Rate of fencing $= Rs. 50$ per meter
$\therefore$ Cost of fencing $= Rs. (182 \times 50)= Rs. 9100$
View full question & answer→Question 73 Marks
Find the diameter of a wheel whose circumference is $176\ cm.$
AnswerLet the radius be $r \ cm$. Diameter $= 2 \times $ Radius$(r) = 2r \ cm$
Circumference of the wheel $=2\pi\text{r}$
$\therefore 2\pi\text{r}=176$
$\Rightarrow 2\text{r}=176\pi$
$\Rightarrow 2\text{r}=176\times\frac{7}{22}$
$\Rightarrow 2\text{r}=56$
Thus, the diameter of the given wheel is $56\ cm.$
View full question & answer→Question 83 Marks
The length and the breadth of a rectangular park are in the ratio $5 : 3$ and its perimeter is $128m$. Find the area of the park.
AnswerLet, the length of the park $= 5x$ and its breadth $= 3x$
So, perimeter of the park $= 2(5x + 3x)$
$\therefore 2(5x + 3x) = 128$
$10x + 6x = 128$
$16x = 128$
$\text{x} =\frac{128}{16}$
$x = 8$
Hence the length of the park $= (5 \times 8) = 40m$
and its breadth $= (3 \times 8) = 24m$
$\therefore$ Area of the park $= (40 \times 24)$
$= 960m^2$
View full question & answer→Question 93 Marks
How many envelopes can be made out of a sheet of paper $3m 24\ cm$ by $1m 72\ cm$, if each envelope requires a piece of paper of size $18\ cm$ by $12\ cm?$
AnswerHere,
Length of the sheet $= 3m 24\ cm = 324\ cm$ and
breadth of the sheet $= 1m 72\ cm = 172\ cm$
Area of the sheet $= (324 \times 172)$
$= 55728\ cm^2$
And, Length of the each envelope $= 18\ cm$ and
Area of the each envelope $= (8 \times 12)$
$= 216\ cm^2$
$\therefore$ Number of the envelopes of the sheet $=\frac{55728}{216}$
$=258$
View full question & answer→Question 103 Marks
Find the distance covered by the wheel of a car in $500$ revolutions if the diameter of the wheel is $77\ cm.$
AnswerRadius of the wheel $=\frac{77}{2}$
$= 38.5\text{cm}$
Circumference of the wheel $=2\pi \text{r}$
$\therefore \text{C}=\Big(2\times \frac{22}{7}\times 38.5\Big)$
$=242\text{cm}$
$=2.42\text{m}$ In revolution, the wheel covers a distance equal to its circumference.
So, distance covered by the wheel in $1$ revolution $= 2.42m$ And,
distance covered by the wheel in $500$ revolution $= (2.42 \times 500)m = 1210m$
View full question & answer→Question 113 Marks
The length and the breadth of a rectangular field are in the ratio $5 : 3$. If its perimeter is 128m, find the dimensions of the field.
AnswerPerimeter of field $= 128m$ Length $+$ Breadth $=\frac{128}{2}$
$=64\text{m}$
Ratio in length and breadth $= 5:3$ Let length $(l) = 5x$
Then breadth $= 3x 5x + 3x = 64$
$\Rightarrow 5x = 64$
$\Rightarrow \text{x}=\frac{64}{8} = 8$
Length of the field $= 5x = 5 x 8 = 40m$ and
breadth $= 3x = 3 \times 8 = 24m$
View full question & answer→Question 123 Marks
The cost of fencing a rectangular field at $Rs. 18$ per metre is $Rs. 1980$. If the width of the field is $23m$, find its length.
AnswerCost of fencing a rectangular field $= Rs. 18 per m$
Total cost $= Rs. 1980$
$\therefore$ Perimeter of the field $=\frac{\text{Total cost}}{\text{Rate}}$
$=\frac{1980}{18}$
$=110\text{m}$ And length + breadth $=\frac{110}{2}$
$=55\text{m}$ Width of the field $= 23m$
Length $= 55 - 23 = 32m$
View full question & answer→Question 133 Marks
The diameter of the wheel of a car is $70\ cm$. How many revolutions will it make to travel $1.65\ km?$
AnswerRedius of the wheel $=\frac{70}{2}$
$=35\text{cm}$
Circumference of the wheel $=2\pi \text{r}$
$\therefore \text{C}=\Big(2\times \frac{22}{7}\times 35\Big)$
$=220\text{cm}$
$1\text{cm}=\frac{1}{220}$ revolution
$\therefore 1\text{km}(100000\text{cm})=\frac{1\times 100000}{220}$ revolution
$\therefore 1.65\text{km}(1.65\times 100000\text{cm})=\frac{1.65\times100000}{220}$
$=750$ revolution.
View full question & answer→Question 143 Marks
Find the cost of fencing a rectangular field $62m$ long and $33m$ wide at $Rs. 16$ per metre.
Answer
Length of rectangular field $(l) = 62m$
And breadth $(b) = 33m$
$\therefore$ Perimeter $= 2(l + b)$
$= 2(62 + 33)$
$= 2 \times 95m$
$= 190m$
Rate of fencing $= Rs. 16$per m
Total cost of fencing the field
$= Rs. 16 \times 190$
$= Rs. 3040$ View full question & answer→Question 153 Marks
The area of a room is $216m^2$ and its breadth is $12m$. Find the length of the room.
AnswerLet the length of the room be $x m.$
Breadth of the room $= 12m$
Area of the room = (Length $\times $ Breadth)
$= (x \times 12)m^2$
It is given that the area of the room is $216m^2$
$\Rightarrow \text{x}\times12=216$
$\Rightarrow \text{x}=\frac{216}{12}$
$=18$
$\therefore$ Length of the rectangle $= 18m.$
View full question & answer→Question 163 Marks
The perimeter of a rectangular field is $360m$ and its breadth is $75m$. Find its length.
AnswerLet the length of the rectangle be $x m.$
Breadth of the rectangle $= 75m$
Perimeter of the rectangle $= 2($ Length $+$ Breadth $) = 2(x + 75)m = (2x + 150)m$
It is given that the perimeter of the field is $360m. $
$\Rightarrow 2x + 150 = 360 $
$\Rightarrow 2x = 360 - 150 $
$\Rightarrow 2x = 210$
$\Rightarrow \text{x}=\frac{210}{2} =105$
So, the length of the rectangle is $105m.$
View full question & answer→Question 173 Marks
Find the area of a rectangle whose length is $36\ cm$ and breadth $15\ cm.$
AnswerLength of the rectangle $= 36\ cm$
Breadth of the rectangle $= 15\ cm$
Area of the rectangle $=$ (Length $\times $ Breadth)sq-units
$= (36 \times 15)cm^2$
$= 540\ cm^2$
View full question & answer→Question 183 Marks
The diameter of a wheel of a car is $77\ cm$. Find the distance covered by the wheel in $500$ revolutions.
AnswerRadius of the wheel =Diameter of the wheel $2$ Diameter of the wheel $2$
$\Rightarrow \text{r}=\frac{77}{2}\text{cm}$ Circumference of the wheel $=2\pi\text{r}$
$=\Big(2\times \frac{22}{7}\times\frac{77}{2}\Big)\text{cm}$ In $1$ revolution,
the wheel covers a distance equal to its circumference.
$\therefore$ Distance covered by the wheel in $1$ revolution $= 242\ cm$
$\therefore$ Distance covered by the wheel in $500$ revolutions $= ( 500 \times 242 )cm = 121000\ cm (100\ cm = 1m) = 1210m$
View full question & answer→Question 193 Marks
A room is $13m$ long and $9m$ broad. Find the cost of carpeting the room with a carpet $75\ cm$ broad at the rate of $Rs. 65$ per meter.
AnswerLength of the room $= 13m = 1300\ cm$ and
its breadth $= 9m = 900\ cm$
Area of the floor of the room $= (1300 \times 900)$
$= 1170000\ cm^2$
Area of the carpet required $= 1170000\ cm^2$
Length of the carpet $=\frac{\text{area of the carpet}}{\text{width of the carpet}}$
$=\frac{1170000}{75}$
$=15600\text{cm}$
$=156\text{m}$
Rate of carpeting $= Rs. 65$ per metre
Cost of carpeting $= Rs. (156 \times 65)$
$= Rs. 10140$
View full question & answer→Question 203 Marks
Two plots of land have the same perimeter. One is a square of side $64m$ and the other is a rectangle of length $70m.$ Find the breadth of the rectangular plot. Which plot has the greater area and by how much?
AnswerPerimeter of the square $= (4 \times 64)$
$= 256m$
Let, the breadth of the rectangle is $x m.$
$\therefore 2(70 + x) = 256$
$140 + 2x = 256$
$2x = 256 - 140$
$\text{x}=\frac{116}{2}$
$x = 58$
Hence, the breadth of the rectangle plot is 58m.
Now, the area of the square plot $= (64)^2= 4096m^2$
And, the area of the rectangle plot $= (70 \times 58) = 4060m^2$
Hence, the square plot is greater than rectangle plot.
View full question & answer→Question 213 Marks
Find the circumference of a circle of radius $7\ cm$. $\Big[\text{Take} \ \pi=\frac{22}{7}\Big]$
AnswerRadius $(r)$ of the given circle $= 7\ cm$
Circumference of the circle, $C$
$=2\pi\text{r}$
$\Big(2\times \frac{22}{7}\times 7\Big)\text{cm}$
$=44\text{cm}$
Hence, the circumference of the given circle is $44\ cm.$
View full question & answer→Question 223 Marks
Each side of a square field measures $21m$, Adjacent to this field, there is a rectangular field having its sides in the ratio $4 : 3.$ If the perimeters of both of the fields are equal, find the dimensions of the rectangular field.
AnswerSide of a square field $(a) = 21m$
Perimeter $= 4a = 4 \times 21 = 84m$
Perimeter of rectangular field $= 84m$
Ratio in length and breadth $= 4 : 3$
Let length $ (l) = 4x$ and breadth $(b) = 3x$
Perimeter $= 2(l + b) $
$\Rightarrow 84 = 4(4x + 3x) $
$\Rightarrow 2 \times 7x $
$\Rightarrow 14x$
$\Rightarrow \text{x}=\frac{84}{14}=6$
$\therefore$ Length $= 4x = 4 \times 6 = 24$
metre And breadth $= 3x = 3 \times 6 = 18$ metre
View full question & answer→