Question

A cone height 8 cm and a base of diameter 9 cm has volume 54π. Find the constant of variation and use it to develop the general formula for the volume of a cone.

Answer 1

Let V be the volume of cone.
Let k be constant of variation
\[V=k \pi r ^{2}h\]
\[54\pi=k \pi \left( \frac{ 9 }{2 } \right)^{2}*8=k \pi \frac{ 81 }{ 4 }*8\]
\[k=\frac{ 54\pi }{ \pi*81*2 }=\frac{ 1 }{ 3 }\]
\[Hence V=\frac{ 1 }{ 3 }\pi r ^{2}h\]