ABC26GN4690 · Area
Subject: General Aptitude · Chapter: Area · Exam: · Marks: · Difficulty:
If the total surface area of a cube is 864 square cm, find the volume of the cube:
(a)$1728 \mathrm{cm}^{3}$
(b)$1624 \mathrm{cm}^{3}$
(c)$144 \mathrm{cm}^{3}$
(d)$1684 \mathrm{cm}^{3}$ [DMRC-Train Operator/Station Controller Exam, 2016]
Answer
Explanation
Each edges of cube $=a \mathrm{cm}$ ∴ Total surface area of cube $=6 a^{2}$ $\Rightarrow 6 a^{2}=864$ $\Rightarrow a^{2}=\frac{864}{6}=144$ $\Rightarrow a=\sqrt{144}=12 \mathrm{cm}$ $$\begin{aligned} \therefore \text { Volume of cube } & =a^{3} \mathrm{cu} . \mathrm{cm} . \\ & =(12 \times 12 \times 12) \mathrm{cu} . \mathrm{cm} . \\ & =1728 \mathrm{cu} . \mathrm{cm} . \end{aligned}$$
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