Volume of a cube

Q.

A cube of side 4 $cm$ is cut into cubes of side 1 $cm$. Calculate the total surface area of all the small cubes.

1. $484c{m}^2$

2. $384c{m}^2$

3. $262c{m}^2$

4. $460c{m}^2$

Q. Question 2
The total surface area of a cube is $96c{m}^2$. The volume of the cube is:

A) $8c{m}^3$
B) $512c{m}^3$
C) $64c{m}^3$
D) $27c{m}^3$​​​​​​​

Q.

Question 8
A solid cube of side 12 cm is cut into eight cubes of equal volume. What will be the side of the new cube? Also, find the ratio between their surface areas.

Q.

The edges of 3 cubes of metal are 3cm, 4cm & 5 cm. they are melted and recasted into a single cube.Find the edges of the new cube.

Q. The side of a cube is 4 cm long. Find the total surface area of the cube.

1. 32 sq. cm
2. 64 sq. cm
3. 96 sq. cm
4. 16 sq. cm

Q.

Three metal cubes with edges 6 cm, 8 cm and 10 cm respectively are melted together and formed into a single cube. Find the volume surface area and diagonal of the new cube.

Q.

The dimensions of a cinema hall are 100 m, 50 m and 18 m. How many persons can sit in the hall, if each person requires $150m^3$ of air?

Q.

If the sum of all the edges of a cube is 36 cm, then the volume $\left(inc{m}^3\right)$ of that cube is

1. 219

2. 9

3. 27

4. 729

Q.

The volumes of the two cubes are in the ratio 64:27. Find the ratio of their surface areas.

1. $16:25$

2. $16:9$

3. $4:3$

4. $9:18$

Q.

If each side of a cube is doubled then its volume

(a) is doubled

(b) becomes $4$ times

(c) becomes $6$ times

(d) becomes $8$ times

Q.

The dimensions of a rectangular box are in the ratio of $2:3:4$ and the difference between the cost of covering it with sheet of paper at the rates of $Rs.8$ and $Rs.9.50$ per $m^2$ is $Rs.1248.$ Find the dimensions of the box.

Q.

If the volumes of two cubes are in the ratio 8:1, then the ratio of their edges is

1. $8:1$

2. None of these

3. $2\sqrt{2}:1$

4. $2:1$

Q.

A child playing with building blocks, which are of the shape of the cubes, has built a structure as shown in the figure. If the edge of each cube is 3 cm, find the volume of the structure built by the child.

Q.

The volume of a cube is $512c{m}^3$ .Its total surface area is

$\left(a\right)256c{m}^2$

$\left(b\right)384c{m}^2$

$\left(c\right)512c{m}^2$

$\left(d\right)64c{m}^2$

Q.

Half cubic metre of gold-sheet is extended by hammering so as to cover an area of 1 hectare. Find the thickness of the gold-sheet.

Q.

If the surface area of a cube is increasing at a rate of $3.6{\text{cm}}^2/\text{sec}$, retaining its shape; then the rate of change of its volume (in ${\mathrm{cm}}^3/\sec$), when the length of a side of the cube is $10\text{cm}$, is

1. $9$

2. $10$

3. $18$

4. $20$

Q.

Two cubes, each of volume $512c{m}^3$ are joined end to end. Find the surface area of the resulting cuboid.

Q.

Find the L.S.A, T.S.A and volume of a cube of side $5cm$.

Q.

A rectangular container, whose base is a square of side 5 cm, stands on a horizontal table, and holds water upto 1 cm from the top. When a cube is placed in the water it is completely submerged, the water rises to the top and 2 cubic cm of water overflows. Calculate the volume of the cube and also the length of its edge.

Q.

Given that 1 cubic cm of marble weighs 0.25 kg, the weight of marble block 28 cm in width and 5 cm thick is 112 kg. Find the length of the block.

Q.

A 4 cm cube is cut into 1 cm cubes. Calculate the total surface area of all the small cubes.

Q.

The side of a cube is 6 cm. The ratio of its surface area and volume is ___ .

Q. Three cubes of metal whose edges are in the ratio 3 : 4 : 5 are melted down in to a single cube whose diagonal is $12\sqrt{3}$ cm. Find the edges of three cubes.

Q.

A solid cube of side $12cm$ is cut into eight cubes of equal volume. What will be the side of the new cube? Also, find the ratio between their surface areas.

Q.

If $A_1,A_{2}and{A}_3$ denote the areas of three adjacent faces of a cuboid, then its volume is

1. $A_1{A}_2{A}_3$

2. $2A_1{A}_2{A}_3$

3. $\sqrt{A_1{A}_2{A}_3}$

4. $\sqrt[3]{3A_1{A}_2{A}_3}$

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.

The cost of constructing a wall 8 m long, 4 m high and 20 cm thick at the rate of Rs 25 per $m^3$ is

1. Rs. 16

2. Rs. 80

3. Rs. 160

4. Rs. 320

Q.

A rectangular tank is 80 m long and 25 m broad. Water-flows into it through a pipe whose cross-section is $25c{m}^2,$ at the rate of 16 km per hour. How much the level of the water rises in the tank in 45 minutes.

Q.

Question 9 (ii)
A right circular cylinder just encloses a sphere of radius r (see figure). Find:

(ii) curved surface area of the cylinder.

Q.

A cube whose volume is $1/8$ cubic centimetre is placed on top of a cube whose volume is 1 $c{m}^3.$ The two cubes are then placed on top of a third cube whose volume is 8 $c{m}^3.$ The height of the stacked cubes is

1. None of these

2. 3.5 cm

3. 3 cm

4. 7 cm