Question

Find the missing measure for a right circular cone given the following information.

Find r if T.A. = 12 and L.A. = 8.

Answer 1

The radius of the cone is:

`r=(2)/(√(\pi))`

Explanation:

The total area of cone is given by:

`T.A.=\pi r(l+r)=\pi rl+\pi r^2=12---------(1)`

where r is the radius of the cone and l is the slant height of the cone.

and the lateral area of cone is given by:

`L.A.=\pi rl=8---------(2)`

Hence, from equation (1) and (2) we have:

`8+\pi r^2=12\\\\\\i.e.\\\\\\\pi r^2=4`

i.e.

`r^2=(4)/(\pi)`

i.e.

`r=(2)/(√(\pi))`