The given solid is a cone with a diameter of

16.5

feet and a slant height of

9.5

feet. To calculate the lateral area, we must know that the lateral area of a right cone is half the product of the circumference of the base and the slant height.

L . A . = \frac{1}{2} \cdot 2 π r \cdot ℓ \Leftrightarrow L . A . = π r ℓ

In this formula,

r

is the radius and

ℓ

is the slant height of the cone. We know that the diameter of the cone's base is

16.5

feet. By dividing by

2,

we get the radius of the base.

r = \frac{1 6 . 5}{2} \Rightarrow r = 8.25 ft

We now know that the radius of the cone is

8.25 ft

and that the slant height of the cone is

9.5 ft .

With this information we are able to calculate the lateral area of the cone. To do so, we will substitute

r = 8.25

and

ℓ = 9.5

into the formula for the lateral area. Let's do it!

L . A . = π r ℓ

SubstituteII

$r = 8.25$ , $ℓ = 9.5$

L . A . = π (8.25) (9.5)

▼

Use a calculator

Multiply

L . A . = π (78.375)

CommutativePropMult

Commutative Property of Multiplication

L . A . = 78.375 π

UseCalc

Use a calculator

L . A . = 246.222324 \dots

RoundDec

Round to $1$ decimal place(s)

L . A . \approx 246.2

The lateral area of the given cone, rounded to the nearest tenth, is

246.2 ft^{2} .

Exercise