The volume of a cube is 512 cm3.
Question:

The volume of a cube is 512 cm3. Its total surface area is
(a) 256 cm2
(b) 384 cm2
(c) 512 cm2
(d) 64 cm2

Solution:

(b) $384 \mathrm{~cm}^{2}$

Suppose that a cm is the edge of the cube.
We have:

$a^{3}=512$

$\Rightarrow a=\sqrt[3]{512}=8 \mathrm{~cm}$

$\therefore$ Total surface area of cube $=6 a^{2} \mathrm{~cm}^{2}$

$=6 \times 8 \times 8 \mathrm{~cm}^{2}=384 \mathrm{~cm}^{2}$

 

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