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

Answer:

The radius of the cone is:

          $r=\dfrac{2}{\sqrt{\pi}}$

Step-by-step 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.

$r^2=\dfrac{4}{\pi}$

i.e.

$r=\dfrac{2}{\sqrt{\pi}}$