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Question
If the volume of a right circular cone of height 9 cm is 48 `pi` cm3, find the diameter of its base.
Solution
The formula of the volume of a cone with base radius ‘r’ and vertical height ‘h’ is given as
Volume of cone = `1/3 pi r^2 h`
It is given that the height of the cone is ‘h’ = 9 cm and that the volume of the cone is 48π cm3
We can now find the radius of base ‘r’ by using the formula for the volume of a cone.
`r^2 =(3( " Volume of the cone" ))/(pih)`
`r^2 = (3(48 pi))/(pi(9))`
`r^2 = 16`
r = 4
Hence the radius of the base of the cone with given dimensions is ‘r’ = 4 cm.
The diameter of base is twice the radius of the base.
Hence the diameter of the base of the cone is 8 cm .
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