1. Warm-up
Find the surface area of the prism below.
3 cm

2. Warm-up
Find the surface area of the prism below.
3 cm

3. Lesson H: Surface Area of Cones & Spheres
Objective:
To find the surface area of a cone
To find the surface area of a sphere

4. Sphere
Cone

5. Slant Height
the height of a lateral face of a cone Variable for slant height: l (cursive lowercase L) l

6. Formulas: Lateral Area of a Cone: LA = rℓ
ℓ: slant height of cone
r: radius of circular base
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 𝜋.
SA = r² + rℓ
SA = (6)² + (6)(18)
SA = 36 + 108
SA = 144 cm2

7. SA = 4πr² FORMULAS: Surface Area of a Sphere: SA = 4r² SA = 4(8)²
1. Find the surface area of the sphere. Leave in terms of 𝜋.
SA = 4r²
SA = 4(8)²
SA = 4(64)
SA = 256 ft2

8. 2. The circumference of a rubber ball is 37. 68 cm
2. The circumference of a rubber ball is cm. Find the surface area to the nearest square inch. Use 3.14 for 𝜋. (Find the radius first.)
C = d
SA = 4r²
37.68 = (3.14)d
SA = 4(3.14)(6)²
SA = 4(3.14)(36)
12 = d
6 = r
SA = in2
SA ≈ 452 in2

9. 3. The surface area of a grapefruit is 314 square inches
3. The surface area of a grapefruit is 314 square inches. Find the circumference of the grapefruit. Use 3.14 for 𝜋. (Find the radius first.)
SA = 4r²
C = d
314= 4(3.14)r²
C = (3.14)(10)
314 = 12.56r²
C = 31.4 in
25 = r²
5 = r
10 = d

10. Assignment:
Worksheet H