Volume of a 3D Object

Q. Find the height of a cuboid whose base area is 180 cm sq. and volume is 900 cm cube?

Q.

The rainfall recorded on a certain day was $5cm$. Find the volume of water that fell on a $2$-hectare field.

Q.

The ratio of radii of two cylinders is $1:2$ and heights are in the ratio $2:3.$ The ratio of their volumes is

1. $1:3$
2. $1:6$
3. $1:9$
4. $2:9$

Q.

The area of a courtyard is 3750 m2. Find the cost of covering it with gravel to a height of 1 cm if the gravel costs 6.40 per cubic metre.

Q.

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.

Q.

A landscaper is creating a rectangular flower bed such that the width is half of the length. The area of the flower bed is $34\mathrm{square}\mathrm{feet}$. Write and solve an equation to determine the width of the flower bed, to the nearest tenth of a foot.

Q.

The volume of a room is $378m^3$ and the area of its floor is $84m^2$. Find the height of the room.

Q.

Given a cylindrical tank, in which situation will you find the surface area and in which situation volume.
(a) To find how much it can hold
(b) Number of cement bags required to plaster it
(c) To find the number of smaller tanks that can be filled with water from it.

Q. The circumference of the base of a Cylindrical vessels is 176cm and it's height is 30 cm How many litres of water can it hold.

Q. Find the volume of each of the given figure, if Volume = Base area $\times$ Height

Q.

The volume of the two cubes are in the ratio 64:27. Find the ratio of their surface area.

1. $9:16$

2. $16:25$

3. $16:9$

4. $4:3$

Q. The volume of a cube is 64 cm${}^3$, then find the surface area.

Q.

A hollow cylindrical tank is filled up with water. The radius of the cylinder is 'r' and height is 1m. The volume of the tank is 15.4L(1000L=1m3). Find the total surface are of the tank.

Q.

In the given figure, a podium is shown, whose each face is rectangular. Find its volume (in $c{m}^3$).

1. $86000c{m}^3$

2. $86400c{m}^3$

3. $86200c{m}^3$

4. $86100c{m}^3$

Q.

Water is pouring into a cubiodal reservoir at the rate of 60 litres per minute. If the volume of reservoir is 108 m³, find the number of hours it will take to fill the reservoir.

Q.

Two solid cones A and B are placed in a cylindrical tube as shown in the figure below. The ratio of their capacities is 2:1. Find the volume of the remaining portion of the cylinder.

1. $406{cm}^3$

2. $396{cm}^3$

3. $376{cm}^3$

4. $386{cm}^3$

Q. The size of a matchbox is 4 cm × 2.5 cm × 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 × 84 cm × 60 cm?

Q. Match the following shape with their volume

1. $a^3$
2. lbh
3. $\pi r^{2}h$
4. 23$\pi r^3$

Q.

Abhishek has three containers:

a)Cylindrical container A having radius r and height 2r
b)Cubical container B having its edge $\frac{3}{4}r$
c)Cuboidal container C having dimensions $r\times \frac{5}{4}r\times \frac{7}{3}r$

The arrangement of the containers in the increasing order of their volumes is

1. A, B, C

2. B, C, A

3. C, A, B

4. cannot be arranged

Q. Question 1
Given a cylindrical tank, in which situation will you find the surface area and in which situation volume.
(a) To find how much it can hold
(b) Number of cement bags required to plaster it
(c) To find the number of smaller tanks that can be filled with water from it.

Q. The volume of a cylinder which exactly fits in a cube of side a is ___

1. $\frac{\pi }{4}{a}^3$
2. $\frac{\pi }{4}{r}^3$
3. $\frac{\pi }{2}{a}^3$
4. $\frac{\pi }{3}{a}^3$

Q.

There is a thin metal plate of length, breadth and thickness 2M mm, 2K mm and 1 mm respectively. If ‘N’ number of plates are placed one on top of the other, what is the object formed and what is its volume in $m{m}^3$?

1. Cuboid, MKN

2. Cuboid, 4MKN

3. Sphere, 4MKN

4. Cylinder, 2 MKN

Q.

Abhishek has three containers:

a)Cylindrical container A having radius r and height 2r

b)Cubical container B having its edge $\frac{3}{4}r$

c)Cuboidal container C having dimensions $r\times \frac{5}{4}r\times \frac{7}{3}r$

The arrangement of the containers in the increasing order of their volumes is

1. A, B, C

2. B, C, A

3. C, A, B

4. cannot be arranged

Q.

The following geometrical shapes are made up of paper. ___ required the least amount of paper and ___ has the maximum volume.

1. Cube, Cylinder

2. Cylinder, Cube

3. Cuboid, Cube
4. Cuboid, Cylinder

Q.

The base area and the area of two adjacent walls of a rectangular box is known. The product of these areas is equal to

1. the square root of the valume

2. The volume of the box

3. twice the volume

4. the square of the volume

Q. Tick (✓) the correct answer:
If the capacity of a cylindrical tank is 1848 m³ and the diameter of its base is 14 m, the depth of the tank is
(a) 8 m
(b) 12 m
(c) 16 m
(d) 18 m

Q.

Find the height of a cuboid whose base area is 180 cm² and volume is 900 cm³?

Q.

There is a thin metal plate of length and breadth $2Mmm$ and $2Kmm$ respectively. Its thickness is $1mm.$ If $‘N^{\prime }$ number of plates are placed one on top of the other, what is the object formed and what is its volume in $m{m}^3$?

1. None of these

2. Cuboid, $MKN$

3. Cuboid, $4MKN$

4. Cube, $4MKN$

Q. Tick (✓) the correct answer:
66 cm³ of silver is drawn into a wire 1 mm in diameter. The length of the wire will be
(a) 78 m
(b) 84 m
(c) 96 m
(d) 108 m

Q. The volume of a cube is $343$ cubic cm. The surface area of the cube is

1. $284{\text{cm}}^2$
2. $290{\text{cm}}^2$
3. $288{\text{cm}}^2$
4. $294{\text{cm}}^2$