Question

A cone of height h cm and base radius r cm is made from a spherical solid of radius 10cm. Show that `r^2=20h-h^2`.?

Answer 1

A cone ABC of height `AD= h cm` and base of radius `CD= r cm` is made from a spherical solid of radius `OA=OB=OC= 10cm`, where `O` is the center of the sphere.

We are to show that `r^2=20h-h^2`.

For right `Delta ODC,angle ODC=90^@`

So by Pythagoras theorem we have

`OC^2=OD^2+CD^2`

`=>10^2=(h-10)^2+r^2`

`=>10^2=h^2-20h+10^2+r^2`

`=>r^2=20h-h^2`