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

Answer:

r = 2 units

Step-by-step explanation:

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

$\text{T.A} =\pi r^2+ \pi r\sqrt{r^2+h^2}$

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

$\text{L.A} = \pi r\sqrt{r^2+h^2}$

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;

$T.A -L.A = \pi r^2+ \pi r\sqrt{r^2+h^2}-\pi r\sqrt{r^2+h^2}$

⇒$12 \pi -8 \pi = \pi r^2$

⇒$4 \pi =\pi r^2$

Divide both sides by $\pi$ we have;

$4 =r^2$

or

$r^2 = 4$

⇒$r= \pm\sqrt{4} =\pm 2$

r cannot be in negative

⇒$r = 2$ units

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