12.3 Notes: Surface Area of Cylinders, Cones and Pyramids Date: 12.3 Notes: Surface Area of Cylinders, Cones and Pyramids   Lesson Objective: Find surface areas of cylinders, cones and pyramids. CCSS: G.MG.3 Apply geometric methods to solve problems You will need: calculator This is Jeopardy!!!: This is the surface area. Take attendance; go over Jeopardy question: 8 min.

Lateral Area, L: The area of one ∆ multiplied by the # of ∆s Lesson 1: Pyramids Lateral Area, L: The area of one ∆ multiplied by the # of ∆s   Base Area, B: The area of the polygon base; B = bh, ½ bh Surface Area, S: S = L + B Pull a stick to have someone read: 2 min.; total = 10

Find the lateral and sur­face areas. Lesson 1: Pyramids Find the lateral and sur­face areas. Pull a stick to have someone read: 2 min.; total = 10

Find the lateral and sur­face areas. Lesson 1: Pyramids Find the lateral and sur­face areas. l 15 8 Pull a stick to have someone read: 2 min.; total = 10

l ² = 8² + 15² l ² = 289 Find the lateral and sur­face areas. Lesson 1: Pyramids Find the lateral and sur­face areas. l ² = 8² + 15² l ² = 289 l 15 l = 17 8 Pull a stick to have someone read: 2 min.; total = 10

l ² = 8² + 15² l ² = 289 Find the lateral and sur­face areas. Lesson 1: Pyramids Find the lateral and sur­face areas. l ² = 8² + 15² l ² = 289 l 15 l = 17 8 L = (½·16·17)·4 = 544 Pull a stick to have someone read: 2 min.; total = 10

l ² = 8² + 15² l ² = 289 Find the lateral and sur­face areas. Lesson 1: Pyramids Find the lateral and sur­face areas. l ² = 8² + 15² l ² = 289 l 15 l = 17 8 L = (½·16·17)·4 = 544 B = 16·16 = 256 Pull a stick to have someone read: 2 min.; total = 10

l ² = 8² + 15² l ² = 289 Find the lateral and sur­face areas. Lesson 1: Pyramids Find the lateral and sur­face areas. l ² = 8² + 15² l ² = 289 l 15 l = 17 8 L = (½·16·17)·4 = 544 B = 16·16 = 256 S = 544 + 256 = 800 ft² Pull a stick to have someone read: 2 min.; total = 10

Lateral Area: L = πrl, l = slant height Base Area: B = πr2 Lesson 2: Cones Lateral Area: L = πrl, l = slant height Base Area: B = πr2 Surface Area: S = L + B, or S = πrl + πr2 Pull a stick to have someone read: 2 min.; total = 10

Find the lateral and sur­face areas. Give answer in terms of π. Lesson 2: Cones Find the lateral and sur­face areas. Give answer in terms of π. Pull a stick to have someone read: 2 min.; total = 10

Lesson 2: Cones Find the lateral and sur­face areas. Give answer in terms of π. l ² = 6² + 8² l ² = 100 l = 10 Pull a stick to have someone read: 2 min.; total = 10

Lesson 2: Cones Find the lateral and sur­face areas. Give answer in terms of π. l ² = 6² + 8² l ² = 100 l = 10 L = πrl = π·8·10 = 80π Pull a stick to have someone read: 2 min.; total = 10

Lesson 2: Cones Find the lateral and sur­face areas. Give answer in terms of π. l ² = 6² + 8² l ² = 100 l = 10 L = πrl = π·8·10 = 80π B = π·8² = 64π Pull a stick to have someone read: 2 min.; total = 10

Lesson 2: Cones Find the lateral and sur­face areas. Give answer in terms of π. l ² = 6² + 8² l ² = 100 l = 10 L = πrl = π·8·10 = 80π B = π·8² = 64π S = 80π + 64π = 144π cm² Pull a stick to have someone read: 2 min.; total = 10

Surface Area, S: S = L + 2B or S = 2πrh + 2πr2. Lesson 3: Cylinders Lateral Area, L: L = 2πrh   Base Area: B = πr2 Surface Area, S: S = L + 2B or S = 2πrh + 2πr2. Pull a stick to have someone read: 2 min.; total = 10

Find the lateral and sur­face areas. Give answer in terms of π. Lesson 3: Cylinders Find the lateral and sur­face areas. Give answer in terms of π. Pull a stick to have someone read: 2 min.; total = 10

Find the lateral and sur­face areas. Give answer in terms of π. Lesson 3: Cylinders Find the lateral and sur­face areas. Give answer in terms of π. L = 2π·8·10 = 160π Pull a stick to have someone read: 2 min.; total = 10

Find the lateral and sur­face areas. Give answer in terms of π. Lesson 3: Cylinders Find the lateral and sur­face areas. Give answer in terms of π. L = 2π·8·10 = 160π B = π·8² = 64π Pull a stick to have someone read: 2 min.; total = 10

Find the lateral and sur­face areas. Give answer in terms of π. Lesson 3: Cylinders Find the lateral and sur­face areas. Give answer in terms of π. L = 2π·8·10 = 160π B = π·8² = 64π S = 160π + 2·64π = 160π + 128π = 288π in² Pull a stick to have someone read: 2 min.; total = 10

A right cone with diameter 18 cm and slant height 5 cm. 12.3: Do I Get It? Yes or No Draw the figure. Find the lateral and surface area. Give circular answers in terms of π. A right cone with diameter 18 cm and slant height 5 cm. A cylinder with diameter 4 cm and height 6 cm. A right square pyramid with base edge length 14 cm and slant height 25 cm. Work on DIGI: 5 min.; total = 55 min

Lesson 2: The Green Bay Cheese Heads   Discuss “Cheeseheads”: 3 min.; total 40, 15 left

Lesson 2: The Green Bay Cheese Heads  

Lesson 2: The Green Bay Cheese Heads  

Lesson 2: The Green Bay Cheese Heads   Suppose you want to make your own Cheese-head. It will be an equilateral triangular prism with sides 2 feet and depth 8 inches. How much paper will you need to make a Cheesehead? SSR: 1 min., field answers on what needs to be done: 2 min; total = 43, 12 left

Lesson 2: The Green Bay Cheese Heads   Suppose you want to make your own Cheese-head. It will be an equilateral triangular prism with sides 2 feet and depth 8 inches. How much paper will you need to make a Cheesehead? Draw a diagram with measures. Calculate the surface area. Work on problem: 4 min.; go over answer: 3 min.; total 50