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

Sphere Cone

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

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

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

2. The circumference of a rubber ball is 37. 68 cm 2. The circumference of a rubber ball is 37.68 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 = 452.16 in2 SA ≈ 452 in2

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

Assignment: Worksheet H