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10-8 Volume of Cylinders Course 1 Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day

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Warm Up Find the volume of each figure described. Course Volume of Cylinders cm 3 1,320 cm 3 1. rectangular prism with length 12 cm, width 11 cm, and height 10 cm 2. triangular prism with height 11 cm and triangular base with base length 10.2 cm and height 6.4 cm

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Problem of the Day The height of a box is half its width. The length is 12 in. longer than its width. If the volume of the box is 28 in, what are the dimensions of the box? 1 in. 2 in. 14 in. 3 Course Volume of Cylinders

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Learn to find volumes of cylinders. Course Volume of Cylinders

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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

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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 352 ft 3. Course Volume of Cylinders

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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 864 cm 3. Course Volume of Cylinders

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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 1,385 in 3. Course Volume of Cylinders

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Check It Out: Example 1A Find the volume V of each cylinder to the nearest cubic unit. Multiply. V The volume is about 565 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

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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

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Check It Out: Example 1C Multiply. V The volume is about 1,231 in 3. Find the radius. r = + 5 h 4 __ r = + 5 = __ Substitute 8 for h. r = + 5 h = 8 in h 4 Write the formula. Replace with 3.14, r with 7, and h with 8. V = r 2 h V 3.14 7 2 8 Course Volume of Cylinders

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Additional Example 2A: Application Ali has a cylinder-shaped pencil holder with a 3 in. diameter and a height of 5 in. Scott has a cylinder- shaped pencil holder with a 4 in. diameter and a height of 6 in. Estimate the volume of each cylinder to the nearest cubic inch. Ali’s pencil holder Write the formula. Replace with 3.14, r with 1.5, and h with 5. Multiply. V in. ÷ 2 = 1.5 in. V 3.14 5 The volume of Ali’s pencil holder is about 35 in 3. Find the radius. V = r 2 h Course Volume of Cylinders

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Additional Example 2B: Application Scott’s pencil holder Write the formula.Multiply.4 in. ÷ 2 = 2 in. The volume of Scott’s pencil holder is about 75 in 3. Find the radius. V = r 2 h Replace with, r with 2, and h with __ V 2 2 __ V = ___ 3 7 __ Course Volume of Cylinders

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Check It Out: Example 2A Sara has a cylinder-shaped sunglasses case with a 3 in. diameter and a height of 6 in. Ulysses has a cylinder-shaped pencil holder with a 4 in. diameter and a height of 7 in. Estimate the volume of each cylinder to the nearest cubic inch. Sara’s sunglasses case Write the formula. Replace with 3.14, r with 1.5, and h with 6. Multiply. V in. ÷ 2 = 1.5 in. V 3.14 6 The volume of Sara’s sunglasses case is about 42 in 3. Find the radius. V = r 2 h Course Volume of Cylinders

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Check It Out: Example 2B Ulysses’ pencil holder Write the formula.Multiply.4 in. ÷ 2 = 2 in. The volume of Ulysses’ pencil holder is about 88 in 3. Find the radius. V = r 2 h Replace with, r with 2, and h with __ V 2 2 __ V 88 Course Volume of Cylinders

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Additional Example 3: Comparing Volumes of Cylinders Find which cylinder has the greater volume. Cylinder 1: V 3.14 12 V = r 2 h V cm 3 Cylinder 2: V 3.14 3 2 6 V = r 2 h V cm 3 Cylinder 2 has the greater volume because cm 3 > cm 3. Course Volume of Cylinders

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Check It Out: Example 3 Find which cylinder has the greater volume. Cylinder 1: V 3.14 10 V = r 2 h V cm 3 Cylinder 2: V 3.14 2 2 4 V = r 2 h V cm 3 Cylinder 1 has the greater volume because cm 3 > cm 3. Course Volume of Cylinders 10 cm 2.5 cm 4 cm

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Lesson Quiz: Part I Find the volume of each cylinder to the nearest cubic unit. Use 3.14 for . Insert Lesson Title Here cylinder b 1, ft ft 3 1,017 ft 3 1, ft 3 Course Volume of Cylinders 1. radius = 9 ft, height = 4 ft 2. radius = 3.2 ft, height = 6 ft 3. Which cylinder has a greater volume? a. radius 5.6 ft and height 12 ft b. radius 9.1 ft and height 6 ft

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Lesson Quiz: Part II Insert Lesson Title Here about 396 in 2 Course Volume of Cylinders 4. Jeff’s drum kit has two small drums. The first drum has a radius of 3 in. and a height of 14 in. The other drum has a radius of 4 in. and a height of 12 in. Estimate the volume of each cylinder to the nearest cubic inch. a. First drum b. Second drum about 603 in 2

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