MCQ
If the diagonal of a cube is 17.32 cm, then its volume is
- ✓$1000 cm^3$
- B$1732 cm^3$
- C$173.2 cm^3$
- D$10000 cm^3$
✓
Answer
Correct option: A.
$1000 cm^3$
(a)
Let the length of each edge of the cube be a cm. Then, its diagonal is $\sqrt{3} a$. Given that
$\begin{array}{ll} & \sqrt{3} a=17.32 \Rightarrow \sqrt{3} a=10 \times 1.732 \Rightarrow \sqrt{3} a=10 \times \sqrt{3} \Rightarrow a=10 \\ \therefore & \text { Volume of the cube }=a^3=10^3 cm^3=1000 cm^3\end{array}$
Let the length of each edge of the cube be a cm. Then, its diagonal is $\sqrt{3} a$. Given that
$\begin{array}{ll} & \sqrt{3} a=17.32 \Rightarrow \sqrt{3} a=10 \times 1.732 \Rightarrow \sqrt{3} a=10 \times \sqrt{3} \Rightarrow a=10 \\ \therefore & \text { Volume of the cube }=a^3=10^3 cm^3=1000 cm^3\end{array}$
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