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

Volume is the number of cubic units needed to fill a space. Course Volume of Prisms

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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 Volume of Prisms

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

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

Additional Example 2A: Finding the Volume of a Triangular Prism Find the volume of each triangular prism. V = BhWrite the formula. V = ( ) __ B = ; h = __ Multiply.V = m 3 Course Volume of Prisms

Additional Example 2B: Finding the Volume of a Triangular Prism Find the volume of the triangular prism. V = BhWrite the formula. V = ( 6.5 7) __ B = 6.5 7; h = __ Multiply.V = ft 3 Course Volume of Prisms

Check It Out: Example 2A Find the volume of each triangular prism. V = BhWrite the formula. V = ( ) __ B = ; h = __ Multiply.V = m m 7 m 4.2 m Course Volume of Prisms

Check It Out: Example 2B Find the volume of each triangular prism. V = BhWrite the formula. V = ( 4.5 9) __ B = 4.5 9; h = __ Multiply. V = ft ft 5 ft 9 ft Course Volume of Prisms

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 Volume of Cylinders

Additional Example 1A: Finding the Volume of a Cylinder Find the volume V of the cylinder to the nearest cubic unit. Write the formula. Replace  with 3.14, r with 4, and h with 7. Multiply. V  V = r 2 h V  3.14  4 2  7 The volume is about ft 3. Course Volume of Cylinders

Additional Example 1B: Finding the Volume of a Cylinder 10 cm ÷ 2 = 5 cmFind the radius.Write the formula. Replace  with 3.14, r with 5, and h with 11. Multiply. V  V = r 2 h V  3.14  5 2  11 The volume is about cm 3. Course Volume of Cylinders

Additional Example 1C: Finding the Volume of a Cylinder Find the radius. r = + 4 h 3 __ r = + 4 = __ Substitute 9 for h.Write the formula. Replace  with 3.14, r with 7, and h with 9. Multiply. V  1, V = r 2 h V  3.14  7 2  9 The volume is about 1, in 3. Course Volume of Cylinders

Check It Out: Example 1A Find the volume V of each cylinder to the nearest cubic unit. Multiply. V  The volume is about ft 3. 6 ft 5 ft Write the formula. Replace  with 3.14, r with 6, and h with 5. V = r 2 h V  3.14  6 2  5 Course Volume of Cylinders

Check It Out: Example 1B Multiply. V  cm ÷ 2 = 4 cm The volume is about 301 cm 3. Find the radius. 8 cm 6 cm Write the formula. Replace  with 3.14, r with 4, and h with 16. V = r 2 h V  3.14  4 2  6 Course Volume of Cylinders

Lesson Quiz Find the volume of each figure. 1. rectangular prism with length 20 cm, width 15 cm, and height 12 cm 2. triangular prism with a height of 12 cm and a triangular base with base length 7.3 cm and height 3.5 cm 3. Find the volume of the figure shown. Insert Lesson Title Here 3,600 cm cm cm 3 Course Volume of Prisms