Question

the lateral surface area of a cube is 64 cm². find the volume of the cube.​

Answer 1

Answer:

64cm^3

Step-by-step explanation:

Lateral surface area = 64 cm^2

4a^2 = 64

a^2 = 64 /4

a^2 = 16

a = under root 16

= 4

Now,

Side of cube = 4 cm

According to the question

Volume of cube = a^3

= 4^3

= 64cm^3

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Answer 2

Volume of cube is 64 cm³.

Given:

• The lateral surface area of a cube is 64 cm².

To find:

• Find the volume of the cube.

Solution:

Formula to be used:

• Lateral surface area of cube$\bf = 4 {a}^{2}$
• Volume of cube $\bf= {a}^{3}$; where, 'a' is side of cube.

Step 1:

Find the side of cube.

Using the formula of lateral surface area.

$4 {a}^{2} = 64$

or

${a}^{2} = \frac{64}{4}$

or

${a}^{2} = 16$

or

$\bf a = \pm4$

Thus,

Side of cube is 4 cm.

Step 2:

Find the volume of cube.

As,

a= 4 cm

Volume of cube$= {4}^{3}$

or

Volume of cube$\bf= 64 \: {cm}^{3}$

Thus,

Volume of cube is 64 cm³.

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