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Question
A solid metallic hemisphere of radius 8 cm is melted and recasted into a right circular cone of base radius 6 cm. Determine the height of the cone.
Solution
For hemisphere,
Radius, r = 8 cm
We know that,
Volume of hemisphere = `2/3 π"r"^3`, where, r = radius of hemisphere
So, we get,
Volume of given hemisphere = `2/3 xx π xx 8^3`
= `(1024/3)π "cm"^3`
Now,
For the cone that is recast from a hemisphere,
Base radius, r = 6 cm
We also know that,
Volume of cone = `1/3 π"r"^2"h"`, where, r is base radius and h is the height of the cone.
So, we get,
Volume of cone = `1/3 π(6)^2"h"` = 12πh
According to the question, we know that,
The volume remains same, when a body is reformed to another body
Volume of cylinder = Volume of cone
12πh = `(1024π)/3`
h = 28.44 cm
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