Volume of a Cube

Q. Total surface area of a cube is 864 sq.cm. Find its volume.

Q.

A swimming pool is 40m long and 15m wide. its shallow and deep ends are 1.5m and 3m deep respectively. If the bottom of the pool slopes uniformly, then amount of water required (in litres) to fill the pool is 13, 50, 000 litres

1. True

2. False

Q.

If there is an error of $\mathrm{k}\%$ in measuring the edge of a cube, then the percent error in estimating its volume is

1. $\mathrm{k}$

2. $3\mathrm{k}$

3. $\frac{\mathrm{k}}{3}$

4. None of these

Q.

A pipe of cross section area 2 $c{m}^2$ delivers 1500 litres of water in 5 minutes. The speed of water in m/s is ___

Q.

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

1. $120c{m}^2$­

2. $145c{m}^2$­

3. $180c{m}^2$­

4. $160c{m}^2$­

Q.

There are two identical cubes. Out of one cube, a sphere of maximum volume (V_S) is cut out. Out of the second cube, a cone of maximum volume (V_C) is cut such that its base lies on one of the faces of the cube. Which one of the following is correct?

1. V_S = V_C

2. V_S = 2V_C

3. 2V_SV_S = 3V_C

4. 3V_S = 4V_C

Q. What is the length of an edge of a cube if its volume is 27 cubic centimetres?

1. 3 cm
2. 9 cm
3. 4 cm
4. 6 cm

Q.

The areas of three adjacent faces of a cuboid are a, b and c. If its volume is V, then V=

1. 

2. 

3. 

4. 

Q.

A storage tank in the form of a cube has water up to its brim. The amount of water in the tank is 4096 m³. After sometime some water was used and , it is found that the depth of water present is 12 m. Find the volume of water used.

1. $1024{\text{m}}^3$

2. $848{\text{m}}^3$
3. $1184{\text{m}}^3$
4. $988{\text{m}}^3$

Q. The area of three adjacent faces of cuboid are 108 cm² ​​​​​, 72cm² ​​​​​​ and 96cm² respectively. Find the volume of cuboid also find the dimension of cuboid

Q.

The lateral surface area of a cube is 256 m². The volume of the cube is ______.

1. $256{\text{m}}^3$

2. $512{\text{m}}^3$

3. $64{\text{m}}^3$

4. $128{\text{m}}^3$

Q.

A rectangular water tank of base $12m\times 10m$ contains water upto a height of 4 m. If the water in the tank is transferred to a square tank of side 8m, find the height of the water level in the tank. (in m)

1. 8

2. 7.5

3. 7

4. 6.5

Q.

The volume of a cube whose edge is 24 m is 1296 m³ .

1. False

2. True

Q. If the areas of three adjacent faces of a cuboid are 8 cm², 18 cm³ and 25 cm³. Find the volume of the cuboid.

Q. If A1, A2, and A3 denote the areas of three adjacent faces of a cuboid, then its volume is

(i) A1 A2 A3

(ii) 2A1 A2 A3

(iii) $\sqrt{A_1{A}_2{A}_3}$

(iv) ${}^3\sqrt{A_1{A}_2{A}_3}$

Q.

Question 7
The lateral surface area of a cube is $256m^2$. The volume of the cube is:

A) $512m^3$
B) $64m^3$
C) $216m^3$
D) $256m^3$​​​​​​​

Q.

Calculate the volume, in cubic centimeters, of a box which is $125$ cm long, $37$ cm wide, and $68$ cm high.

Report your answer with correct significant figures in cubic centimeters.

Q. A metallic sheet is of the rectangular shape with dimensions $48cm\times 36cm$. From each one of its corners, a square of $8cm$ is cutoff. An open box is made of the remaining sheet. Find the volume of the box.

1. $510{cm}^3$
2. $2150c{m}^3$
3. $512c{m}^3$
4. $5120c{m}^3$

Q. The lateral surface area of a cube is $256c{m}^2$. The volume of the cube is:

Q.

Three iron cubes with edges 3 cm, 4 cm and 5 cm respectively, are melted and cast into a single cube. Find the edge of the bigger cube formed.

1. 9

2. 10

3. 6

4. 8

Q.

There are $13.5\mathrm{\pi }$ cubic inches of blue sand and $9\mathrm{\pi }$ cubic inches of red sand in the cylindrical container. How many cubic inches of white sand are in the container? Round your answer to the nearest tenth?

Q. The length of the longest rod that can be fitted in a cubical vessel of edge 10 cm long, is

(a) 10 cm

(b) 10$\sqrt{2}$ cm

(c) 10$\sqrt{3}$ cm

(d) 20 cm

Q. If a solid cube of dimensions $10cm\times 10cm\times 10cm$ is put inside a cuboid of dimensions $10cm\times 20cm\times 30cm$, then what's the volume of space remaining inside the cuboid?

1. 6000 $c{m}^3$
2. 5000 $c{m}^3$
3. 1000 $c{m}^3$
4. 7000 $c{m}^3$

Q. A cuboidal vessel is 10 m long and 8 m wide. How high must it be made to hold 380 cubic meters of a liquid?

Q. Find the length of each side of a cube if its volume is $512c{m}^3$.

Q.

The water in a cubical tank of side 10m is transferred to completely fill a cuboidal tank of length 5m and breadth 10 and height h. Then the height of the cuboidal tank (in metres) is ___

Q. Ravish wanted to make a temporary shelter for his car by making a box like structure with tarpaulin that covers all the four sides and the top of the car (with the front faces as flap which can be rolled up). Assuming that the stitching margins are very small, and therefore negligible, how much tarpaulin would be required to make the shelter of height $12.5m$ with base dimensions $4m\times 3m$?

Q.

Q. The lateral surface area of a cube is 256 m². The volume of the cube is
(a) 64 m³
(b) 216 m³
(c) 256 m³
(d) 512 m³

Q.

The area of one face of a cube is $100m^2$. Find the volume of the cube.

1. 3000 $m^3$

2. 2000 $m^3$

3. 1000 $m^3$

4. 343 $m^3$