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

Let `r` is radius of circular cone and `h_c` is its height.

Radius of both cone and hemisphere will be same.

It is given that , `h_c = `diameter of the ballon

`:. h_c = 2r`

Also, total height, `h = h_c+r = 3r`

`=>r = h/3`

Now, total volume of the baloon,

`V = 1/3pir^2h_c+2/3pir^3`

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