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What will be the volume of a cube, if its surface area is $900 cm ?$

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3375 cm 3

3475 cm 3

3735 cm 3

3575 cm 3

answer is A.

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Detailed Solution

It is given that the cube’s lateral surface area is 900 cm.
If

a

is the side length of a cube, then its lateral surface area is

4 a 2,

and its volume is

a 3 .

∴ 4 a 2 = 900 ⇒ a 2 = 9004 ⇒ a 2 = 225 ⇒ a = 15 cm

Therefore, the volume of the cube can be calculated as,

V = 153 ⇒ V = 15 × 15 × 15 cm 3 ⇒ V = 3375 cm 3

Thus, the volume of the cube is

3375 cm 3 .

Hence, option (1) is correct.

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