Question : Find the volume of a sphere having a diameter of 6 mm, in terms of $\pi$.
Option 1: $12 \pi ~\mathrm{mm}^3$
Option 2: $24 \pi ~\mathrm{mm}^3$
Option 3: $64 \pi~ \mathrm{mm}^3$
Option 4: $36 \pi ~\mathrm{mm}^3$
Correct Answer: $36 \pi ~\mathrm{mm}^3$
Solution :
Given,
Diameter = $6~\mathrm{mm}$
⇒ Radius = $\frac62$ = $3~\mathrm{mm}$
Volume of a sphere = $\frac43\pi r^3$, where $r$ is the radius of the sphere
⇒ Volume = $\frac43\pi \times3^3$
= $4\pi\times3\times3$
= $36 \pi ~\mathrm{mm}^3$
Hence, the correct answer is $36 \pi ~\mathrm{mm}^3$.
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