Surface Area of a Cube

Q. Question 3
Find the side of a cube whose surface area is $600c{m}^2$.

Q.

A cube of side $5cm$ is painted on all its faces. If it is sliced into $1$ cubic centimetre cubes, then how many $1$ cubic centimetre cubes will have exactly one of their faces painted?

(a) $27$

(b) $42$

(c) $54$

(d) $142$

Q.

Question 2

A cube of side 4 cm is cut into 1 cm cubes. What is the ratio of the surface areas of the original cube and cut-out cubes ?
(a) 1 : 2 (b) 1 :3 (c) 1 : 4 (d) 1 : 6

Q.

The diagonal of a cube is $9\sqrt{3}$cm long. Its total surface area is

(a) $243c{m}^2$

(b) $486c{m}^2$

(c) $324c{m}^2$

(d) $648c{m}^2$

Q.

The volume of a cube is $729c{m}^3$. Find its surface area.

Q.

Question 11

The volume of a cube is $64c{m}^3.$ Its surface area is
(a) $16c{m}^2$ (b) $64c{m}^2$
(c) $96c{m}^2$ (d) $128c{m}^2$

Q.

Two cubes have their volumes in the ratio $1:27$. The ratio of their surface areas is

(a) $1:3$

(b) $1:9$

(c) $1:27$

(d) none of these

Q.

If the length of each edge of a cube is doubled, how many times does its volume become? How many times does its surface area become?

Q.

The volume of a cube is 343 cm'. Its total surface area is

(a) $196c{m}^2$

(b) $49c{m}^2$

(c) $294c{m}^2$

(d) $147c{m}^2$

Q. Question 6
Describe how the two figures below are alike and how they are different. Which box has larger lateral surface area?

Q. Two cubes each of edge 6 cm are joined face to face. Find the surface area of the cuboid thus formed.

Q.

Question 53

State whether the following statement is true or false:

The areas of any two faces of a cube are equal.

Q.

Question 58

State whether the following statement is true or false:

A cube of side 3 cm painted on all its faces, when sliced into 1 cubic cm cubes, will have exactly 1 cube with none of its faces painted.

Q.

If each side of a cube is doubled, its surface area

(a) is doubled

(b) becomes 4 times

(c) becomes 6 times

(d) becomes 8 times

Q.

A cube of side $5cm$ is cut into as many $1cm$ cubes as possible. What is the ratio of the surface areas of the original cube to that of the sum of the surface areas of the smaller cubes?

Q.

The length of the diagonals of a cube is $8\sqrt{3}cm$. Find its:
i) Edge
ii) Total surface area
iii) Volume

Q.

Calculate the surface area of a cube of edge $4cm$ . what is the volume?

Q.

Find the surface area of a cube whose volume is
(i) $343m^3$ (ii) $216d{m}^3$

Q.

Question 8

The surface area of the three coterminus faces of a cuboid are 6, 15 and $10c{m}^2$, respectively. The volume of the cuboid is
(a) $30c{m}^3$ (b) $40c{m}^3$ (c) $20c{m}^3$ (d) $35c{m}^3$

Q.

Find the surface area of a wooden box whose shape is of a cube, and if the edge of the box is 12 cm.

Q. 16 If each edge of a cube is increased by 50%, then find the percentage increase in its surface area.

Q.

Length of each side of a cube is increased by 25%. Then the percentage increase in volume will be ___.

Q.

Find the surface area of a cube whose edge is
(i) 1.2 m (ii) 27 cm (iii) 3 cm (iv) 6 m (v) 2.1 m

Q. Question 7(i)
If each edge of a cube is doubled
How many times will its surface area increase?

Q.

If the volume of a cube is 12167, then find the length of its sides through estimation. [3 MARKS]

Q.

If each edge of a cube is doubled:

(i) How many times will its surface area increase?

(ii) How many times will its volume increase? [4 MARKS]

Q.

Question 60

State whether the following statement is true or false:

The surface area of a cube formed by cutting a cuboid of dimensions $2\times 1\times 1$ in 2 equal parts, is 2 sq. units.

Q. The cost of painting a cube is ₹ $2/c{m}^2$. How much does it cost if a cube of side 3 cm is painted on all its sides?

1. ₹ 64
2. ₹ 54
3. ₹ 128
4. ₹ 108

Q.

Question 124

Work out the surface area of the following shape.

Q. What is the difference between total surface area and lateral surface area of a cube whose edge length is 1 cm?

1. $2c{m}^2$
2. $6c{m}^2$
3. $4c{m}^2$
4. $3c{m}^2$