find the surface area of the right cone given the radius and slant height shown. you can write your answer…

Explanation:

Step1: Recall the formula for the surface area of a cone

The surface area ( S ) of a right cone is given by the formula ( S=\pi r^2+\pi r l ), where ( r ) is the radius and ( l ) is the slant height.

Step2: Identify the values of ( r ) and ( l )

From the diagram, the radius ( r = 6 ) and the slant height ( l=18 ).

Step3: Substitute the values into the formula

First, calculate ( \pi r^2 ): ( \pi\times(6)^2=\pi\times36 = 36\pi )

Then, calculate ( \pi r l ): ( \pi\times6\times18=\pi\times108 = 108\pi )

Now, add these two results together to get the surface area: ( S=36\pi + 108\pi=144\pi )

If we want to round to the nearest hundredth, we know that ( \pi\approx3.14159 ), so ( 144\pi\approx144\times3.14159\approx452.39 )

Answer:

The surface area of the right cone is ( 144\pi ) (or approximately ( 452.39 ))