A balloon in the form of a right circular cone surmounted by a hemisphere, having a diameter equal to the height of the cone, is being inflated. How fast is its volume changing with respect to tis total height `h ,` when `h=9c mdot`

Explanation

`H=h+r`


`Rightarrow H=3 r[because h=2 r]`


`Rightarrow frac{d H}{d t}=3 frac{d r}{d t}`


When `H=9 quad {cm}, r=3 {cm}`


Volume `=frac{1}{3} pi r^{2} h+frac{2}{3} pi r^{3}`


Substituting `{h}=2 r`


`Rightarrow V=frac{2}{3} pi r^{3}+frac{2}{3} pi r^{3}`


`Rightarrow V=frac{4}{3} pi r^{3}`


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