Question

Total surface area of a cube is 1014cm^2. It's volume will be :

a) 2197 cm^3
b) 2297 cm^3
c) 2179 cm^3
d) 2117 cm^3

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Answer 1

`V=2197\ cm^3`

Explanation:

Surface Area and Volume of a Cube

Given a cube of side length a, the surface area is:

`A = 6a^2`

The volume is calculated as:

`V=a^3`

It's given the surface area of a cube:

`A=1014\ cm^2`

We can find the side length a by solving for a:

`\displaystyle a=\sqrt{(A)/(6)}`

`\displaystyle a=\sqrt{(1014)/(6)}`

`\displaystyle a=√(169)`

a = 13 cm

Now compute the volume:

`V=13^3`

`\boxed{V=2197\ cm^3}`

Answer: a) 2197 cm^3