10 7 Volume of Prisms Warm Up Problem

10 -7 Volume of Prisms Warm Up Problem of the Day Lesson Presentation Course 1

10 -7 Volume of Prisms Volume is the number of cubic units needed to fill a space. Course 1

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10 -7 Volume of Prisms It takes 10, or 5 · 2, centimeter cubes to cover the bottom layer of this rectangular prism. There are 3 layers of 10 cubes each to fill the prism. It takes 30, or 5 · 2 · 3, cubes. Volume is expressed in cubic units, so the volume of the prism is 5 cm · 2 cm · 3 cm = 30 cm 3. Course 1

10 -7 Volume of Prisms Additional Example 1: Finding the Volume of a Rectangular Prism Find the volume of the rectangular prism. 13 in. 11 in. 26 in. V = lwh V = 26 • Write the formula. 11 • V = 3, 718 in 3 Course 1 13 l = 26; w = 11; h = 13 Multiply.

10 -7 Volume of Prisms Check It Out: Example 1 Find the volume of the rectangular prism. 16 in. 12 in. 29 in. V = lwh V = 29 • Write the formula. 12 • V = 5, 568 in 3 Course 1 16 l = 29; w = 12; h = 16 Multiply.

10 -7 Volume of Prisms To find the volume of any prism, you can use the formula V= Bh, where B is the area of the base, and h is the prism’s height. So, to find the volume of a triangular prism, B is the area of the triangular base and h is the height of the prism. Course 1

10 -7 Volume of Prisms Additional Example 2 A: Finding the Volume of a Triangular Prism Find the volume of each triangular prism. V = Bh 1 __ V = ( • 3. 9 2 • V = 10. 14 m 3 Course 1 1. 3) • 4 Write the formula. 1 __ B= • 3. 9 • 1. 3; h = 4. 2 Multiply.

10 -7 Volume of Prisms Additional Example 2 B: Finding the Volume of a Triangular Prism Find the volume of the triangular prism. V = Bh 1 __ V = ( • 6. 5 2 V = 136. 5 ft Course 1 • 3 7) • 6 Write the formula. 1 __ B= • 6. 5 • 7; h = 6. 2 Multiply.

10 -7 Volume of Prisms Check It Out: Example 2 A Find the volume of each triangular prism. 7 m 1. 6 m 4. 2 m V = Bh 1 __ V = ( • 4. 2 2 • V = 23. 52 m 3 Course 1 1. 6) • 7 Write the formula. 1 __ B= • 4. 2 • 1. 6; h = 7. 2 Multiply.

10 -7 Volume of Prisms Check It Out: Example 2 B Find the volume of each triangular prism. 9 ft 5 ft 4. 5 ft V = Bh 1 __ V = ( • 4. 5 2 • V = 101. 25 ft 3 Course 1 9) • 5 Write the formula. 1 __ B= • 4. 5 • 9; h = 5. 2 Multiply.

10 -8 Volume of Cylinders To find the volume of a cylinder, you can use the same method as you did for prisms: Multiply the area of the base by the height. volume of a cylinder = area of base height The area of the circular base is r 2, so the formula is V = Bh = r 2 h. Course 1

10 -8 Volume of Cylinders Additional Example 1 A: Finding the Volume of a Cylinder Find the volume V of the cylinder to the nearest cubic unit. V = r 2 h Write the formula. V 3. 14 42 7 Replace with 3. 14, r with 4, and h with 7. Multiply. V 351. 68 The volume is about 351. 68 ft 3. Course 1

10 -8 Volume of Cylinders Additional Example 1 B: Finding the Volume of a Cylinder 10 cm ÷ 2 = 5 cm Find the radius. V = r 2 h Write the formula. V 3. 14 52 11 Replace with 3. 14, r with 5, and h with 11. Multiply. V 863. 5 The volume is about 863. 5 cm 3. Course 1

10 -8 Volume of Cylinders Additional Example 1 C: Finding the Volume of a Cylinder h +4 r = __ 3 9 +4=7 r = __ 3 V = r 2 h V 3. 14 72 9 V 1, 384. 74 Find the radius. Substitute 9 for h. Write the formula. Replace with 3. 14, r with 7, and h with 9. Multiply. The volume is about 1, 384. 74 in 3. Course 1

10 -8 Volume of Cylinders Check It Out: Example 1 A Find the volume V of each cylinder to the nearest cubic unit. 6 ft 5 ft V = r 2 h Write the formula. V 3. 14 62 5 Replace with 3. 14, r with 6, and h with 5. Multiply. V 565. 2 The volume is about 565. 2 ft 3. Course 1

10 -8 Volume of Cylinders Check It Out: Example 1 B 8 cm 6 cm 8 cm ÷ 2 = 4 cm Find the radius. V = r 2 h Write the formula. V 3. 14 42 6 Replace with 3. 14, r with 4, and h with 16. V 301. 44 Multiply. The volume is about 301 cm 3. Course 1

10 -7 Volume Insert Lesson of Prisms Title Here Lesson Quiz Find the volume of each figure. 1. rectangular prism with length 20 cm, width 15 cm, and height 12 cm 3, 600 cm 3 2. triangular prism with a height of 12 cm and a triangular base with base length 7. 3 cm and height 3. 5 cm 153. 3 cm 3 3. Find the volume of the figure shown. 38. 13 cm 3 Course 1