Exercise 14 Page 828

Let's first calculate the lateral area and then use the result to calculate the surface area.

Lateral Area

The given solid is a cone.

To calculate the lateral area of a cone, we can use the known formula where r is the radius of the base and l is the slant height of the cone. L=π rl We are given that the radius r of the cone is 4inches and the slant height l is 11inches By substituting r with 4 and l with 11 into the formula, we can calculate L.

L=π rl

SubstituteII

r= 4, l= 11

L=π( 4)( 11)

▼

Simplify right-hand side

Multiply

Multiply

L=44π

UseCalc

Use a calculator

L=138.230076...

RoundDec

Round to 1 decimal place(s)

L≈ 138.2

The lateral area of the cone is about 138.2 square inches.

Surface Area

To calculate the surface area of a pyramid, we need to calculate the sum of the lateral area L and the area of the base B. S=L+B Recall that the base of the cone is a circle. We can find its area using the formula B = π r^2.

B = π r^2

Substitute

r= 4

B = π* 4^2

▼

Simplify right-hand side

CalcPow

Calculate power

B = π * 16

UseCalc

Use a calculator

B = 50.265482...

RoundDec

Round to 1 decimal place(s)

B≈ 50.3

Finally, let's substitute L= 138.2 and B= 50.3 into the formula for the surface area and calculate it.

S=L+B

SubstituteII

L= 138.2, B= 50.3

S=138.2+50.3

AddTerms

Add terms

S=188.5

The surface area of the pyramid is about 188.5 square inches.