Question : How many solid spherical balls each of 33 cm radius can be made out of a solid spherical ball of radius 66 cm?
Option 1: 8
Option 2: 4
Option 3: 7
Option 4: 3
Correct Answer: 8
Solution :
Volume of a sphere $=\frac{4}{3}\pi r^3$, where $r$ is the radius
The volume of the larger sphere with a radius of 66 cm,
$V_{\text{large}} = \frac{4}{3} \pi (66)^3$
The volume of the smaller sphere with a radius of 33 cm,
$V_{\text{small}} = \frac{4}{3} \pi (33)^3$
$\therefore$ The number of smaller spheres that can be made out of the larger sphere $ = \frac{V_{\text{large}}}{V_{\text{small}}} = \frac{(66)^3}{(33)^3} = 8$
Hence, the correct answer is 8.
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