Warm-up

Find the surface area of the prism below.

3 cm

Warm-up

Find the surface area of the prism below.

3 cm

Lesson H: Surface Area of Cones & Spheres

Objective: • To find the surface area of a cone • To find the surface area of a sphere

Cone Sphere

Slant Height

the height of a lateral face of a cone

Variable for slant height: l (cursive lowercase L)

l

ℓ: slant height of cone

r: radius of circular baseFormulas:

Lateral Area of a Cone: LA = rℓ

Surface Area of a Cone: SA = r² + rℓ

1. Find the surface area of the cone in terms of .

SA = r² + rℓSA = (6)² + (6)(18)

SA = 36 + 108

SA = 144 cm2

SA = 4πr²

FORMULAS:

Surface Area of a Sphere:

1. Find the surface area of the sphere. Leave in terms of .

SA = 4r²SA = 4(8)²

SA = 4(64)

SA = 256 ft2

2. The circumference of a rubber ball is 37.68 cm. Find the surface area to the nearest square inch. Use 3.14 for . (Find the radius first.)

SA = 4r²SA = 4(3.14)(6)²

SA = 4(3.14)(36)

SA = 452.16 in2

C = d37.68 = (3.14)d

12 = d

6 = r

SA 452 in2

3. The surface area of a grapefruit is 314 square inches. Find the circumference of the grapefruit. Use 3.14 for . (Find the radius first.)

SA = 4r²314= 4(3.14)r²

314 = 12.56r²

25 = r²

C = dC = (3.14)(10)

C = 31.4 in

5 r

10 d

√ √

Assignment:

Worksheet H