Volume of a Cube

Q.

Question 29

A cube of side 4 cm is painted on all its sides. If it is sliced in 1 cubic cm cubes, then number of such cubes that will have exactly two of their faces painted is ___

Q. Find the length of the side of a cube whose total surface area is $486c{m}^2$.

1. 81 cm
2. 486 cm
3. 18 cm
4. 9 cm

Q.

A solid cube of metal each of whose sides measures $2.2cm$ is melted to form a cylindrical wire of radius $1mm$. Find the length of the wire so obtained.

Q.

A solid cubical block of fine wood costs $Rs.256$ at $Rs.500$ per $m^3$. Find its volume and the length of each side.

Q. Question 7(ii)
If each edge of a cube is doubled
how many times will its volume increase?

Q. How many solid cubes of 3 cm edge can be cut out of a solid cube of 18 cm edge?

1. 232
2. 216
3. 484
4. 36

Q.

A metal sheet $27cm$ long, $8cm$ broad and $1cm$ thick is melted into a cube. The side of the cube is

(a) $6cm$ (b) $8cm$ (c) $23cm$ (d) $24cm$

Q. What is the volume of a cube of side 10 cm?

1. 10000 $c{m}^3$
2. 1000 $c{m}^3$
3. 100 $c{m}^3$
4. 10 $c{m}^3$

Q.

The length breadth and height of a room are in the ratio $3:2:1$. If the breadth and height are halved while the length is doubled, then total area of the four walls of the room will,

1. Remain the same

2. Decrease by $30\%$

3. Decrease by $15\%$

4. Decrease by $18.75\%$

Q.

Question 25

Two cubes have volumes in the ratio 1 : 64. The ratio of the area of a face of first cube to that of the other is
a) 1 : 4
b) 1 : 8
c) 1 : 16
d) 1 : 32

Q.

The total surface area of a cube is $150c{m}^2$. Its volume is

(a) $216c{m}^3$

(b) $125c{m}^3$

(c) $64c{m}^3$

(d) $1000c{m}^3$

Q. If the volume of the cube is 216 $c{m}^3$, then the length of the edge of the cube is

1. 6 cm
2. 5 cm
3. 4 cm
4. 7 cm

Q.

Question 93

If the length of each edge of a cube is tripled, what will be the change in its volume?

Q.

The cost of painting the whole surface area of a cube at the rate of 10 palse per $c{m}^2$ is 264.60. Then, the volume of the cube is

(a) $6859c{m}^3$

(b) $9261c{m}^3$

(c) $8000c{m}^3$

(d) $10648c{m}^3$

Q. What will happen to the volume of a cube, if its edge is
$\left(i\right)$. Halved

Q.

Find the volume, lateral surface area and the total surface area of a cube each of whose 14c edges measures:

(i) 7 m

(ii) 5.6 cm

(iii) 8 dm 5 cm

Q.

Question 30

A cube of side 5 cm is cut into 1 cm cubes. The percentage increase in volume after such cutting is ___

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

1. $8c{m}^3$
2. $512c{m}^3$
3. $64c{m}^3$
4. $27c{m}^3$

Q.

A metal cube of edge 12 cm is melted and formed into three smaller cubes. If the edges of the two smaller cubes are 6 cm and 8 cm, find the edge of the third smaller cube.

Q.

Question 26

The surface areas of the six faces of a rectangular solid are 16, 16, 32, 32, 72 and 72 sq cm. The volume of the solid (in cubic cm) is
a) 192
b) 384
c) 480
d) 2592

Q.

Express 1729 as the sum of cube of two numbers. [2 MARKS]

Q. If the length of each edge of a cube is doubled, what is the change in its total surface area?

Q.

Three equal cubes are placed adjacently in a row. Find the ratio of the total surface area of the new cubiod to that of the sum of the surface areas of the three cubes.

Q. The number of solid cubes of side 3 m can be cut from a solid cuboid measuring 18 m × 12 m × 9 m is .

1. 72
2. 36
3. 64
4. 81

Q. The length of the longest rod that can be fitted in a cubical room of edge length 4 cm is:

1. 8.66 m
2. 5.196 m
3. 6.928 m
4. 7.264 m

Q.

Find the volume of a cube whose side is
(i) 4 cm (ii) 8 cm (iii) 1.5 dm (iv) 1.2 m (v) 25 mm

Q. How to find the cube of 0.3 ?

Q.

A cube A has side thrice as long as that of cube B ? What is the ratio of the volume of cube A to that of cube B?

Q.

An edge of a variable cube is increasing at the rate of $10$ cm/s. How fast the volume of the cube will increase when the edge is $5$cm long?

1. $750c{m}^3/s$

2. $75c{m}^3/s$

3. $150c{m}^3/s$

4. $25c{m}^3/s$

Q.

The number of small cubes of edge of $10cm$ that can be accommodated in a cubical box of edge $1m$ is

1. 10

2. 100

3. 1000

4. 110