Question : A solid sphere of radius 4 cm is melted and cast into the shape of a solid cone of height 4 cm. The radius of the base of the cone is______.
Option 1: 8 cm
Option 2: 4 cm
Option 3: 6 cm
Option 4: 10 cm
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Correct Answer: 8 cm
Solution :
Radius of sphere = 4 cm
Volume of sphere = $\frac{4}{3} \pi r^3$ = $\frac{4}{3} \pi (4)^3$
Let the radius of the base of the cone be $R$ and the height is 4 cm.
Now volume of cone = $\frac{1}{3} \pi r^2h$ = $\frac{1}{3} \pi R^2 \times 4$
According to the question,
The volume of cone = Volume of a sphere
$⇒\frac{1}{3} \pi R^2 \times 4 = \frac{4}{3} \pi (4)^3$
$⇒R^2=(4)^3 = 64$
$⇒R=8$ cm
Hence, the correct answer is 8 cm.
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