Surface Area & Volume

Surface Area of Cones

Lesson 15

Write the surface area formula for each solid.

1. Prism

2. Cylinder

3. Pyramid

4. Find the surface area of each solid. Use 3.14 for .a. b.

2(LW + WH + LH)

2 π r h + 2 π r2

Lateral Area + Base Area

Target: Calculate the surface area of cones.

The lateral area (LA) of a cone is equal to one-half the circumference (C) of the

base times the slant height (l) of the cone.

LA = Cl = πrl2

1

The surface area of a cone is equal to the sum of the lateral area (LA) and the

area of the base (B).

SA = LA + B

SA = πrl + πr2

Jenny serves snow cones by putting flavored ice in apaper cone-shaped cup. Find the lateral area of the snowcone cup. Use 3.14 for π.

Write the formula. LA = πrl Substitute known values. LA ≈ (3.14)(8)(10) Multiply. LA ≈ 251.2

The lateral area of the snow cone cup is 251.2 square centimeters.

Find the surface area of thecone. Use 3.14 for π.

Find the length of the radius. 12 ÷ 2 = 6 Find the area of the base. πr2 ≈ (3.14)(6)2 ≈ 113.04 Write the formula. SA = πrl + B Substitute values. SA ≈ (3.14)(6)(9) + (113.04) Multiply, then add. SA ≈ 169.56 + 113.04 ≈ 282. 6

The surface area is approximately 282.6 in2.

1. The slant height of a cone is 4 feet. The radius of the cone is 3 feet. Use 3.14 for .

a) Find the lateral area of the cone.

b) Find the surface area of the cone.

2. The lateral area of the cone is 541.65 mm². Find the length of the radius. Use 3.14 for π.

How is lateral area calculated for a prism, cylinder, pyramid and cone?

What is similar about finding the surface area of a cone and a pyramid?