A child consumed an ice cream of inverted right-circular conical shape from the top and left only 12.5% of the cone for her mother. If the height of the ice cream-cone was 8 cm, what was the height of the remaining ice cream-cone?
Explanation:
Cone left for the mother after the child consumes = 12.5% = 1/8
Now, the change in the volume of the coin is proportional to the cube of change in radius.
Thus the radius of the cone that is left = r(1/8)1/3 = r/2
If the radius of the base and height of the cone left be r1 and h1, then
8 × π × r12 × h1 = π × r2 × h
∴ 8 × (r/2)2 × h1 = r2 × 8
∴ h1 = 4
Hence, option (d).
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