Calculate Volume of Prisms & Cylinders

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Presentation transcript:

Calculate Volume of Prisms & Cylinders 9.4 Calculate Volume of Prisms & Cylinders

V = Bh Where B = area of the base And h = height Volume of a Prism V = Bh Where B = area of the base And h = height

Find the volume of the box by determining Example 1 Find the Volume of a Rectangular Prism Find the volume of the box by determining how many unit cubes fit in the box. SOLUTION The base is 5 units by 3 units. So, 3 · 5, or 15 unit cubes are needed to cover the base layer. There are 4 layers. Each layer has 15 cubes. So, the total number of cubes is 4 · 15, or 60. ANSWER The volume of the box is 60 cubic units. 3

Find the volume of the prism. Example 2 Find the Volume of a Prism Find the volume of the prism. a. b. SOLUTION a. V = Bh Write the formula for volume of a prism. = (7 · 4) · 5 Area of rectangular base = l · w = 7 · 4. = 140 Simplify. ANSWER The volume is 140 cubic inches. 4

Write the formula for volume of a prism. Area of triangular base = Example 2 Find the Volume of a Prism b. V = Bh Write the formula for volume of a prism. Area of triangular base = 1 2 – · 8 · 6. = · 8 · 6 · 3 = 72 Simplify. ANSWER The volume is 72 cubic feet. 5

Find the volume of the prism. Checkpoint Find Volume of Prisms 2. Find the volume of the prism. 1. 3.

Find the volume of the prism. Checkpoint Find Volume of Prisms Find the volume of the prism. 1. ANSWER 216 ft3 2. ANSWER 125 cm3 3. ANSWER 245 in.3

Volume of a Cylinder V = πr2h

How do the radius and height of the mug compare to the radius Example 3 Compare Volumes of Cylinders How do the radius and height of the mug compare to the radius and height of the dog bowl? a. How many times greater is the volume of the bowl than the volume of the mug? b. SOLUTION The radius of the mug is 2 inches and the radius of the dog bowl is 6 inches. The radius of the bowl is three times the radius of the mug. The height of the mug is the same as the height of the bowl. a. 9

Write the formula for volume. Substitute for r and for h. Example 3 Compare Volumes of Cylinders b. Volume of mug Volume of dog bowl V = πr2h Write the formula for volume. = π(22)(4) = π(62)(4) Substitute for r and for h. = 16π Simplify. = 144π To compare the volume of the bowl to the volume of the mug, divide the volume of the bowl by the volume of the mug. –––––––––––––– Volume of bowl Volume of mug 144π 16π ––––– = = 9 ANSWER The volume of the bowl is nine times the volume of the mug. 10

Checkpoint Find Volume of Cylinders Find the volume of the cylinder. Round your answer to the nearest whole number. 6. 4. 5.

Checkpoint Find Volume of Cylinders Find the volume of the cylinder. Round your answer to the nearest whole number. 4. ANSWER 38 ft3 5. ANSWER 16 in.3 6. ANSWER 126 m3

Review Find the surface area of the solid. If necessary, round your answer to the nearest whole number. 1. 150 m2 ANSWER 2. 2286 mm2 ANSWER

Find the lateral area of a right cone with radius 5 inches and slant height 22 inches. Round your answer to the nearest whole number. 3. 346 in.2 ANSWER

Worksheet 9.4A