Sample QuestionsVolume and Surface Area of Solids questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
The diagonal of a cube measures $4\sqrt{3}\text{cm}.$ Its volume is:
- A
$8 \mathrm{~cm}^3$
- B
$16 \mathrm{~cm}^3$
- C
$27 \mathrm{~cm}^3$
- ✓
$64 \mathrm{~cm}^3$
Answer: D.
View full solution →Five equal cubes, each of edge $5\ cm,$ are placed adjacent to each other. The volume of the cuboid so formed, is:
- A
$ 125 \mathrm{~cm}^3 $
- B
$ 375 \mathrm{~cm}^3 $
- C
$ 525 \mathrm{~cm}^3 $
- ✓
$ 625 \mathrm{~cm}^3 $
Answer: D.
View full solution →The ratio of the radii of two cylinders is $2 : 3$ and the ratio of their heights is $5 : 3.$ The ratio of their volumes will be:
- A
$4 : 9$
- B
$9 : 4$
- ✓
$20 : 27$
- D
$27 : 20$
Answer: C.
View full solution →The diameter of a cylinder is $14\ cm$ and its curved surface area is $220\ cm^2$. The volume of the cylinder is:
- ✓
$770 \mathrm{~cm}^3$
- B
$1000 \mathrm{~cm}^3$
- C
$1540 \mathrm{~cm}^3$
- D
$6622 \mathrm{~cm}^3$
Answer: A.
View full solution →The surface area of a $(10\ cm \times 4\ cm \times 3\ cm)$ brick is:
- A
$ 84 \mathrm{~cm}^2 $
- B
$ 124 \mathrm{~cm}^2$
- ✓
$164 \mathrm{~cm}^2 $
- D
$ 180 \mathrm{~cm}^2 $
Answer: C.
View full solution →Assertion (A): If the volumes of two cubes are in the ratio 1 : 8 then their surface areas are in the ratio 1 : 4.
Reason (R): If the surface areas of two cubes are in the ratio 1 : 4 then their edges are in the ratio 1 : 2.
- A
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
- B
Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
- C
Assertion (A) is true but Reason (R) is false.
- D
Assertion (A) is false but Reason (R) is true.
View full solution →Assertion (A): Total surface area of a cylinder = $2 \pi r(h+r)$, where r = radius of base and h = height of cylinder.
Reason (R): Total surface area of a cylinder = curved surface area + area of circular base + area of circular top.
- A
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
- B
Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
- C
Assertion (A) is true but Reason (R) is false.
- D
Assertion (A) is false but Reason (R) is true.
View full solution →Assertion (A): If a rectangular paper of length a and width b is rolled along its length then a cylinder is formed.
Reason (R): The height of the cylinder so formed is a and its circumference is b.
- A
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
- B
Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
- C
Assertion (A) is true but Reason (R) is false.
- D
Assertion (A) is false but Reason (R) is true.
View full solution →Assertion (A): Volume of a cylinder = circumference of circular base $\times$ height.
Reason (R): Volume of a cylinder $=\pi r^2 h$, where $r=$ radius of base and $h=$ height of cylinder.
- A
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
- B
Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
- C
Assertion (A) is true but Reason (R) is false.
- D
Assertion (A) is false but Reason (R) is true.
View full solution →Assertion (A): If the length of each edge of a cube is doubled then its volume becomes 8 times.
Reason (R): To calculate the volume, we multiply the edge thrice and so the multiplying factor also gets multiplied thrice.
- A
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
- B
Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
- C
Assertion (A) is true but Reason (R) is false.
- D
Assertion (A) is false but Reason (R) is true.
View full solution →Find the surface area of a chalk box, whose length, breadth and height are $18\ cm, 10\ cm$ and $8\ cm$ respectively.
View full solution →How many soap cakes each measuring $7cm \times 5cm \times 2.5cm$ can be placed in a box of size $56cm \times 40cm \times 25cm?$
View full solution →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?
View full solution →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?
View full solution →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.
View full solution →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.
View full solution →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?
View full solution →Find the volume, lateral surface area and the total surface area of the cuboid whose dimensions are:
Length $= 24m,$ breadth $= 25\ cm$ and height $= 6m$
View full solution →A wooden cylindrical pole is $7\ m$ high and its base radius is $10\ cm$. Find its weight if the wood weighs $225\ kg$ per cubic metre.
View full solution →A milk tank is in the form of a cylinder whose radius is $1.5\ m$ and height is $10.5\ m$. Find the quantity of milk in litres that can be stored in the tank.
View full solution →Find the volume, curved surface area and total surface area of the cylinders whose dimensions are: Radius of the base $= 14\ dm$ and height $= 15\ m$
View full solution →Find the volume, lateral surface area and the total surface area of the cuboid whose dimensions are:
Length $= 15\ m$, breadth $= 6\ m$ and height $= 9\ dm.$
View full solution →Mohanlal bought a shop to start a hardware store. The shop is 12 m long, 4 m wide and 3 m high. Mohanlal paid for it at the rate of ₹ 3500 per sq metre floor area and had to pay 8% of the total cost as stamp duty. To make the shop ready for use, he has to get it painted and the fabrication work done.
1. How much did Mohanlal pay for the shop?
(a) ₹ 168000$\quad$(b) ₹ 181440$\quad$(c) ₹ 504000$\quad$(d) ₹ 544320$\quad$
2. If Mohanlal utilizes one third of the shop to store paint boxes of dimensions 12 cm x 8 cm x 4 cm, how many boxes can he store?
(a) 37500 $\quad$(b) 75000 $\quad$(c) 105000 $\quad$(d) 125000 $\quad$
3. Mohanlal gets the two long side walls and the rear wall of the shop painted. How much will he pay for it at the rate of 96 per sq metre?
(a) ₹ 8064$\quad$(b) ₹ 9216$\quad$(c) ₹ 10368$\quad$(d) ₹ 13824$\quad$
4. To serve his customers and passers-by, Mohanlal installed a cylindrical water cooler tank in front of his shop. If the tank is 1 m high and 28 cm wide, how many litres of water it can hold?
(a) 38.5 $\quad$(b) 61.5 $\quad$(c) 77 $\quad$(d) 92.4 $\quad$
View full solution →Fill in the blanks. If $l, b, h$ be the length, breadth and height of a cuboid, then its lateral surface area $=$ ________ sq units.
View full solution →Fill in the blanks. If $r$ is the radius of the base and $h$ be the height of a cylinder, then its lateral surface area is ________ sq units.
View full solution →Fill in the blanks. If $r$ is the radius of the base and $h$ be the height of a cylinder, then its volume is __________ cubic units.
View full solution →Fill in the blanks. If $l, b, h$ be the length, breadth and height of a cuboid, then its whole surface area $=$ ________ sq units.
View full solution →Fill in the blanks.
If each side of a cube is a, then its lateral surface area is ______ sq units.