Question : Two metallic balls P and Q are such that the diameter of P is four times the diameter of Q. What is the ratio between the volumes of P and Q?
Option 1: 32 : 1
Option 2: 16 : 1
Option 3: 8 : 1
Option 4: 64 : 1
Correct Answer: 64 : 1
Solution :
Given: Two metallic balls P and Q are such that the diameter of P is four times the diameter of Q.
Use the formula, The volume of the sphere of radius $r$ is $\frac{4}{3}\pi r^3$.
Let the diameters of P and Q be $2r_1$ and $2r_2$ respectively.
According to the question,
$2r_1=4\times 2r_2$
⇒ $r_1=4r_2$
The ratio between the volumes of P and Q = $\frac{\frac{4}{3}\times \pi \times ({4r_2})^3}{\frac{4}{3}\times \pi \times (r_2)^3}=\frac{64r_2^3}{r_2^3}=64:1$
Hence, the correct answer is 64 : 1.
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