Question

Find the missing measure for a right circular cone given the following information. Find r if T.A. = 12pi and L.A. = 8pi

Answer 1

ARea of base = TA - LA = 4pi

pi r^2 = 4 pi where r is radius of base.

r^2 = 4

so r = 2 Answer

Answer 2

r = 2 units

Explanation:

Total area(T.A) of the circular cone is given by:

`\text{T.A} =\pi r^2+ \pi r√(r^2+h^2)`

Lateral surface area(L.A) of the circular cone:

`\text{L.A} = \pi r√(r^2+h^2)`

where

r is the radius and h is the height of the circular cone.

As per the statement:

`T.A = 12 \pi` and
`L.A = 8 \pi`

then;

`T.A -L.A = \pi r^2+ \pi r√(r^2+h^2)-\pi r√(r^2+h^2)`

⇒
`12 \pi -8 \pi = \pi r^2`

⇒
`4 \pi =\pi r^2`

Divide both sides by
`\pi` we have;

`4 =r^2`

or

`r^2 = 4`

⇒
`r= \pm√(4) =\pm 2`

r cannot be in negative

⇒
`r = 2` units

Therefore, radius of the circular cone is, r = 2 units