Question:
The lateral surface area of a cube is 256 m2. The volume of the cube is
(a) 512 m3
(b) 64 m3
(c) 216 m3
(d) 256 m3
Solution:
(a) Given, lateral surface area of a cube = 256 m2
We know that, lateral surface area of a cube = 4 x (Side)2
=> 256 = 4 x (Side)2
=> (Side)2 = 256/4 = 64
=> Side = √64 = 8 m
[taking positive square root because side is always a positive quantity]
Now, volume of a cube = (Side)3 = (8)3 = 8 x 8 x 8 = 512 m3
Hence, the volume of the cube is 512 m3.
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