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If the radius of a sphere is doubled, how many times does its volume becomes ?
Answer & Solution
Correct Answer:
Option
D
Let the original radius be r
Then, original volume = $$\frac{4}{3}\pi {r^3}$$
New area = 2r
∴ New volume :
$$\eqalign{ & = \frac{4}{3}\pi {\left( {2r} \right)^3} \cr & = 8 \times \frac{4}{3}\pi {r^3} \cr & = 8 \times {\text{Original volume}} \cr} $$
Then, original volume = $$\frac{4}{3}\pi {r^3}$$
New area = 2r
∴ New volume :
$$\eqalign{ & = \frac{4}{3}\pi {\left( {2r} \right)^3} \cr & = 8 \times \frac{4}{3}\pi {r^3} \cr & = 8 \times {\text{Original volume}} \cr} $$
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