Volume of a Cube

Q.

The perimeter of one face of a cube is 20 cm. Find the volume of the cube.

1. $125c{m}^3$
2. $400c{m}^3$
3. $250c{m}^3$
4. $625c{m}^3$

Q. The volume of a dice cube with side length 2 cm is ________ .

1. 4 cc
2. 16 cc
3. 6 cc
4. 8 cc

Q. The surface area of the shoe box given below is

1. 392 sq in
2. 292 sq in
3. 218 sq in

Q.

The total surface area of a cube is $216c{m}^2$. Find its volume.

Q. Water present in this container is to be transferred to a cubical container (in the shape of a cube). What should be the length of the new container?

Q. The outer area of the given wooden box needs to be painted. Find the surface area of the box to be painted.

1. 268 sq in
2. 568 sq in
3. 460 sq in
4. 140 sq in

Q.
The total surface area of the cube of side length $5$ units as shown in the diagram above is, while its volume is .

1. $150$ sq. units
2. $125$ cubic units
3. $625$ cubic units
4. $100$ sq. units

Q. The volume of a cuboid with length $x$, breadth $y$, and height $h$ is ____.

1. $x\times y\times h$
2. $x^2+y^2+z^2$
3. $x+y+h$
4. $2\times (x+y+h)$

Q.
The side length of the largest cube that can fill up the rectangular prism as shown above is .

1. $2$ units
2. $3$ units
3. $0.5$ units

Q. A cubical water tank holds $125$ litres of water. What will be the cost of whitewashing its outer walls, if the rate is $\$10/$ cm${}^2$ ?

Q. For a cube of side length $8$ cm. Match the following.

1. $512$ cubic units
2. $384$ sq. units
3. $256$ sq. units

Q. The volume of a dice cube with side length 2 cm is ________ .

1. 16 cc
2. 6 cc
3. 8 cc
4. 4 cc

Q. The edge of one cube is $5.2$ cm while that of another cube is $7.2$ cm. What will be the difference in their volumes?

Q. The outer area of the given wooden box needs to be painted. Find the surface area of the box to be painted.

1. 460 sq in
2. 268 sq in
3. 140 sq in
4. 568 sq in

Q.

A closed box has a square base with side length $\mathrm{L}\mathrm{feet}$ and height $\mathrm{h}\mathrm{feet}$.

Given that the volume of the box is $39\mathrm{cubic}\mathrm{feet}$, express the surface area of the box in terms of $\mathrm{L}$ only.

Q. Find the volume of a cube (in $c{m}^3$) with side $=6cm.$

Q. In how much time, the cylindrical pond having radius $3.5$ m and depth $7$m can be filled by a tap which gives the water at the rate of $60$ litres per minute?

1. $320$ hours
2. $32.06$ hours
   
3. $12.06$ hours
4. $3.06$ hours

Q. Find the capacity (in litres) of a cylindrical storage tank of height $1.2m$ and base diameter $35cm$.

Q. A carton holds $45$ cubical gift boxes with a side of $6$ cm each. If the length and width of the carton is $20$ cm and $15$ cm respectively, what will be its height (in cm) ?

Q. The volume of cube of side $.01m$ in ${cm}^3$ is :

1. $1$
2. $.0001$
3. $.001$
4. $.000001$

Q. Hydraulic engineers in the United States often use, as a unit of volume of water, the $acre-foot$, defined as the volume of wa-ter that will cover $1$ acre of land to adepth of $1$ ft.A severe thun-derstorm dumped $2.0$ in. of rain in $30$ min on a town of area $26k{m}^2$.What volume of water, in acre-feet, fell on the town?

Q. The breadth of a room is twice its height and half its length and volume of the room is $512$ cub meter. How high is the roof of the room?

Q.
Find the number of cubes of side length equals $2$ units that can fill up the rectangular prism as shown.

1. 6

Q.
The number of cubes having side length $0.5$ units that can occupy the prism, as shown above, is .

1. $432$
2. $400$
3. $512$

Q. The value of a sphere is $\frac{4}{3}\pi r^{3}c.c.$ What is the ratio of the volume of a cube to that of a sphere which will fit inside the cube?

1. $4:3\pi$
2. $2:\pi$
3. $6:\pi$
4. $8:\pi$

Q. Two identical cubes each of volume $64$ $c{m}^3$ are joined together end to end. What is the surface area of the resulting cuboid?

Q. A wall 4 m long, 3 m high and 0.4 m thick is to be built. How many bricks 20 cm long, 12 cm broad and 10 cm thick will be required?

Q. A rectangular container, whose base is a square of side $12$ cm, contains sufficient water to submerge a rectangular solid $8$ cm $\times$ $6$ cm $\times$ $3$ cm. Find the rise in level of the water in the container when the solid is in it.

1. $1$ cm
2. $2$ cm
3. $3$ cm
4. $4$ cm

Q. If 70% of the volume from a 10 cm cubical container is poured into a cuboidal vessel of length 20 cm, breadth 15 cm and height 10cm, what fraction of the cuboidal vessel is occupied ?

Q. If the total surface area of a cube is 486 $c{m}^2$, find the volume of the cube.