Exercise 16 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 diameter of the cone's base is 3.4cm. By dividing by 2, we get the radius of the base. r=3.4/2= 1.7cm We are also given that the slant height is 6.5cm. By substituting r= 1.7 and l= 6.5 into the formula, we can calculate L.

L=π rl

SubstituteII

r= 1.7, l= 6.5

L=π( 1.7)( 6.5)

▼

Simplify right-hand side

UseCalc

Use a calculator

L=34.714598...

RoundDec

Round to 1 decimal place(s)

L≈ 34.7

The lateral area of the cone is approximately 34.7cm^2.

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= 1.7

B = π( 1.7)^2

▼

Simplify right-hand side

UseCalc

Use a calculator

B = 9.079202...

RoundDec

Round to 1 decimal place(s)

B≈ 9.1

Finally, let's substitute L= 34.7 and B= 9.1 into the formula for the surface area and calculate it.

S=L+B

SubstituteII

L= 34.7, B= 9.1

S= 34.7+ 9.1

AddTerms

Add terms

S=43.8

The surface area of the pyramid is about 43.8cm^2.