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: $36 \pi ~\mathrm{mm}^3$
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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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Question : What is the area of a circle with a diameter of $12~\text{mm}$?
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