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MATHS [2 Mark Question Answer]

Volume & Surface Area of Solids · ICSE STD 8 (ICSE - English Medium). 29 questions.

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[2 Mark Question Answer]

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29 questions · timed · auto-graded

Question 12 Marks
A swimming pool $70 m \times 44 m \times 3 m$ is filled by water issuing from a pipe of diameter 35 cm at 6 m per second. How many hours does it take to fill the pool?
Answer
$4 \frac{4}{9}$ hours
[Hint : Volume of water released in 1 second $=\pi \times\left(\frac{0.35}{2}\right)^2 \times 6 m^3$
$\therefore$ Required time $=\frac{70 \times 44 \times 3}{5 \times\left(\frac{0.35}{2}\right)^2 \times 6}$ seconds.]
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Question 22 Marks
The total surface area of a circular cylinder is $1320 cm^2$ and its radius is 10 cm. Find the height of the cylinder.
Answer
11 cm
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Question 32 Marks
The sum of the radius of the base and the height of a solid cylinder is 37 m. If the total surface area of the cylinder is $1628 m^2$, find its volume.
Answer
$4620 m^3$
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Question 42 Marks
The total surface area of a solid cylinder is $462 cm^2$ and its curved surface area is one-third of its total surface area. Find the volume of the cylinder.
Answer
$539 cm^3$
$\begin{array}{l}{\left[\text { Hint }: 2 \pi r h+2 \pi r^2=462 \text { and } 2 \pi r h=\frac{462}{3}=154 \Rightarrow 2 \pi r^2=462-154=308 \Rightarrow r=7 cm\right.} \\ \left.\quad \text { Now, } 2 \pi r h=154 \Rightarrow h=\frac{154}{2 \times 22 \times 7}=0.5 cm\right]\end{array}$
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Question 52 Marks
The curved surface area of a cylinder is $4400 cm^2$ and the circumference of its base is 110 cm. Find the height and the volume of the cylinder.
Answer
$40 cm, 38500 cm^3$
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Question 62 Marks
A cylindrical tank has a capacity of $6160 m^3$. Find its depth, if its radius is 14 m. Also find the cost of painting its curved surface at ₹ $30$ per $m ^2$.
Answer
10 m, ₹ 26400
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Question 72 Marks
Find the weight of a solid cylinder of radius 10.5 cm and height 60 cm, if the material of the cylinder weighs 5 grams per $cm ^3$.
Answer
103.95 kg
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Question 82 Marks
Find the curved surface area and the total surface area of the cylinder for : h = 5 m and r = 35 m
Answer
$110000 cm^2, 117700 cm^2$
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Question 92 Marks
Find the curved surface area and the total surface area of the cylinder for : h = 35 cm and r = 21 cm
Answer
$4620 cm^3, 7392 cm^2$
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Question 102 Marks
Find the curved surface area and the total surface area of the cylinder for : h = 32 cm and r = 10.5 cm
Answer
$2112 cm^2, 2805 cm^2$
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Question 112 Marks
Find the curved surface area and the total surface area of the cylinder for : h = 30 cm and r = 14 cm
Answer
$2640 cm^2, 3872 cm^2$
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Question 122 Marks
A well with 10 m inside diameter is dug 8.4 m deep. Earth taken out of it is spread all around it to a width of 7.5 m to form an embankment. Find the height of the embankment.
Answer
1.6 m
$\begin{array}{l}{\left[\text { Hint }: \text { Volume of earth dug out }=\left(\frac{22}{7} \times 5 \times 5 \times 8.4\right) m ^3\right.} \\ \left.\text { Area of the embankment }=\frac{22}{7} \times\left\{(12.5)^2-5^2\right\} m ^2\right]\end{array}$
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Question 132 Marks
A 20 m deep well with diameter 7 m is dug up and the earth from digging is spread evenly to form a platform $22 m \times 14 m$. Determine the height of the platform.
Answer
2.5 m
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Question 142 Marks
The volume of a cuboid is $1296 m^3$. Its length is 24 m and its breadth and height are in the ratio $3: 2$. Find the breadth and height of the cuboid.
Answer
9 m, 6 m
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Question 152 Marks
A classroom is 10 m long, 6.4 m broad and 5 m high. If each student be given $1.6 m^2$ of the floor area, how many students can be accommodated in the room? How many cubic metres of air would each student get?
Answer
$40,8 m^3$
$\begin{array}{l}{\left[\text { Hint : } \text { Number of students }=\left(\frac{\text { Area of the floor in } m^2}{1.6}\right)\right.} \\ \left.\text { Air available to each student }=\left(\frac{\text { Volume of the room in } m^3}{\text { Number of students }}\right) m ^3\right]\end{array}$
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Question 162 Marks
How many planks each measuring 5 m by 24 cm by 10 cm can be stored in a place 15 m long, 4 m wide and 60 cm deep?
Answer
300
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Question 172 Marks
A wall of length 13.5 m, width 60 cm and height 1.6 m is to be constructed by using bricks, each of dimensions 22.5 cm by 12 cm by 8 cm. How many bricks will be needed?
Answer
6000
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Question 182 Marks
Three cubes of metal with edges 5 cm, 4 cm and 3 cm respectively are melted to form a single cube. Find the lateral surface area of the new cube formed.
Answer
$144 cm^2$
[Hint : Sum of the volumes of the three cubes = volume of the new cube
$\Rightarrow 5^3+4^3+3^3=x^3$.]
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Question 192 Marks
A solid piece of metal in the form of a cuboid of dimensions $24 cm \times 18 cm \times 4 cm$ is melted down and recasted into a cube. Find the length of each edge of the cube.
Answer
12 cm
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Question 202 Marks
Find the capacity of a rectangular cistern whose length is 6 m, breadth 2.5 m and depth 1.4 m. Also find the area of the iron sheet required to make the cistern.
Answer
$21 m^3, 53.8 m^2$
[Hint : Area of iron sheet required $=$ Total surface area of the cistern]
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Question 212 Marks
The internal dimensions of a closed box, made up of iron 1 cm thick, are 24 cm by 18 cm by 12 cm. Find the volume of iron in the box.
Answer
$2096 cm^3$
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Question 222 Marks
The external dimensions of a wooden box, open at the top are 54 cm by 30 cm by 16 cm. It is made of wood 2 cm thick. Calculate
(i) the capacity of the box
(ii) the volume of wood.
Answer
(i) $18200 cm^3$
(ii) $7720 cm^3$
[Hint : Since, the box is open, so the internal dimensions of the box are $(54-2 \times 2) cm$, $(30-2 \times 2) cm$ and $(16-2) cm$.]
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Question 232 Marks
A closed wooden box 80 cm long, 65 cm wide and 45 cm high, is made up of wood 2.5 cm thick. Find
(i) the capacity of the box
(ii) the weight of the box, if $100 cm^3$ of wood weighs 8 grams.
Answer
(i) $180000 cm^3$
(ii) 4.32 kg
[Hint : Internal dimensions of the box are $(80-2 \times 2 \cdot 5) cm ,(65-2 \times 2 \cdot 5) cm$ and $(45-2 \times 2 \cdot 5) cm$.]
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Question 242 Marks
A river 2 m deep and 40 m wide is flowing at the rate of 4.5 km per hour. How many cubic metres of water runs into the sea per minute?
Answer
$6000 m^3$
[Hint : Volume of water flown in 1 hour $=(4.5 \times 1000 \times 2 \times 40) m ^3$.]
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Question 252 Marks
If the areas of the three adjacent faces of a cuboidal box are $120 cm^2, 72 cm^2$ and $60 cm^2$ respectively, then find the volume of the box.
Answer
$720 cm^3$
[Hint : Let the dimensions of the box be $l$ cm, $b$ cm and $h$ cm. Then, $l \times b=120 cm^2$, $b \times h=72 cm^2, l \times h=60 cm^2$. Multiplying, we get : $l^2 \times b^2 \times h^2=120 \times 72 \times 60$.]
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Question 262 Marks
The length, breadth and height of a cuboid are in the ratio $7: 6: 5$. If the surface area of the cuboid is $1926 cm^2$, find its dimensions. Also find the volume of the cuboid.
Answer
$21 cm, 18 cm, 15 cm, 5670 cm^3$
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Question 272 Marks
An assembly hall is 45 m long, 30 m broad and 16 m high. It has five doors, each measuring 4 m by 3.5 m and four windows 2.5 m by 1.6 m each. Find
(i) the cost of papering its walls at the rate of ₹ 35 per $m ^2$;
(ii) the cost of carpeting its floor at the rate of ₹ 154 per $m ^2$.
Answer
(i) ₹ 80990
(ii) ₹ 207900
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Question 282 Marks
The length, breadth and height of a room are 8 m, 6.5 m and 3.5 m respectively. Find
(i) the area of 4 walls of the room.
(ii) the area of the floor of the room.
Answer
(i) $101.5 m^2$
(ii) $52 m^2$
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Question 292 Marks
Find the volume, the total surface area and the lateral surface area of the cuboid having :
(i) length = 24 cm, breadth = 16 cm and height = 7.5 cm
(ii) length = 10 m, breadth = 35 cm and height = 1.2 m
Answer
(i) $2880 cm^3, 1368 cm^2, 600 cm^2$
(ii) $4.2 m^3, 31.84 m^2, 24.84 m^2$
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