Question

The total surface area of a cube is 864 cm². Its volume is
(a) 3456 cm³
(b) 432 cm³
(c) 1728 cm³
(d) 3456 cm³

Answer 1

(c) 1728 cm³
Let the edge of the cube be a.
Total surface area of the cube = 6a²
Therefore,
$$\begin{gathered} 6a^2=864 \\ {a}^2=144 \\ a=12\text{cm} \end{gathered}$$
Therefore, volume of the cube = a³
$$\begin{gathered} =\left(12\times 12\times 12\right){\text{cm}}^3 \\ =1728{\text{cm}}^3 \end{gathered}$$