what is the lateral area and surface area?

Question

a cone with radius 8 m and height that is 1 m less than twice the radius

Answer 1

Hi, Molly,

Let's start with figuring out the height. It's given to be 1m less than twice the radius.

An equation for this would be

h = 2r-1

Now plug in the given value for the radius, and get

h = 2(8)-1

h=15m

From here use the formulas for the lateral surface area and then for the area of the base.

A_L= π(r) √(h²+r²)

A_{L= π(8) √(15}²₊₈²)

A_L=427.2566009m²

The complete surface area is the lateral area plus the area of the base. The base is a circle, so we use the formula

A_B=π r²

A_{B=π (64)}

_AB=201.0619298m²

Add the two areas to get 628.3185307m²

Best wishes!