Volume of Cylinders 10-9 Warm Up Problem of the Day Course 1 Warm Up Problem of the Day Lesson Presentation

Volume of Cylinders 10-9 Warm Up Course 1 10-9 Volume of Cylinders Warm Up Find the volume of each figure described. 1. rectangular prism with length 12 cm, width 11 cm, and height 10 cm 1,320 cm3 2. triangular prism with height 11 cm and triangular base with base length 10.2 cm and height 6.4 cm 359.04 cm3

Volume of Cylinders 10-9 Problem of the Day Course 1 10-9 Volume of Cylinders 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? 3 1 in.  2 in.  14 in.

Course 1 10-9 Volume of Cylinders Learn to find volumes of cylinders.

Course 1 10-9 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 r2, so the formula is V = Bh = r2h.

Additional Example 1A: Finding the Volume of a Cylinder Course 1 10-9 Volume of Cylinders Additional Example 1A: Finding the Volume of a Cylinder Find the volume V of the cylinder to the nearest cubic unit. A. V = r2h Write the formula. V  3.14  42  7 Replace  with 3.14, r with 4, and h with 7. V  351.68 Multiply. The volume is about 352 ft3.

Additional Example 1B: Finding the Volume of a Cylinder Course 1 10-9 Volume of Cylinders Additional Example 1B: Finding the Volume of a Cylinder B. 10 cm ÷ 2 = 5 cm Find the radius. V = r2h Write the formula. V  3.14  52  11 Replace  with 3.14, r with 5, and h with 11. V  863.5 Multiply. The volume is about 864 cm3.

Additional Example 1C: Finding the Volume of a Cylinder Course 1 10-9 Volume of Cylinders Additional Example 1C: Finding the Volume of a Cylinder C. r = + 4 h 3 __ Find the radius. r = + 4 = 7 9 3 __ Substitute 9 for h. V = r2h Write the formula. V  3.14  72  9 Replace  with 3.14, r with 7, and h with 9. V  1,384.74 Multiply. The volume is about 1,385 in3.

Volume of Cylinders 10-9 Try This: Example 1A Course 1 10-9 Volume of Cylinders Try This: Example 1A Find the volume V of each cylinder to the nearest cubic unit. A. 6 ft 5 ft V = r2h Write the formula. V  3.14  62  5 Replace  with 3.14, r with 6, and h with 5. V  565.2 Multiply. The volume is about 565 ft3.

Volume of Cylinders 10-9 Try This: Example 1B B. 8 cm 6 cm Course 1 10-9 Volume of Cylinders Try This: Example 1B B. 8 cm 6 cm 8 cm ÷ 2 = 4 cm Find the radius. V = r2h 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 cm3.

Volume of Cylinders 10-9 Try This: Example 1C C. h r = + 5 4 h = 8 in Course 1 10-9 Volume of Cylinders Try This: Example 1C C. h r = + 5 4 h = 8 in r = + 5 h 4 __ Find the radius. r = + 5 = 7 8 4 __ Substitute 8 for h. V = r2h Write the formula. V  3.14  72  8 Replace  with 3.14, r with 7, and h with 8. V  1230.88 Multiply. The volume is about 1231 in3.

Course 1 10-9 Volume of Cylinders 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. A. Ali’s pencil holder 3 in. ÷ 2 = 1.5 in. Find the radius. V = r2h Write the formula. Replace  with 3.14, r with 1.5, and h with 5. V  3.14  1.52  5 V  35.325 Multiply. The volume of Ali’s pencil holder is about 35 in3.

Volume of Cylinders 10-9 Additional Example 2B: Application Course 1 10-9 Volume of Cylinders Additional Example 2B: Application B. Scott’s pencil holder 4 in. ÷ 2 = 2 in. Find the radius. V = r2h Write the formula. Replace  with , r with 2, and h with 6. 22 7 __ V   22  6 22 7 __ V  = 75 528 7 ___ 3 __ Multiply. The volume of Scott’s pencil holder is about 75 in3.

Volume of Cylinders 10-9 Try This: Example 2A Course 1 10-9 Volume of Cylinders Try This: 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. A. Sara’s sunglasses case 3 in. ÷ 2 = 1.5 in. Find the radius. V = r2h Write the formula. Replace  with 3.14, r with 1.5, and h with 6. V  3.14  1.52  6 V  42.39 Multiply. The volume of Sara’s sunglasses case is about 42 in3.

Volume of Cylinders 10-9 Try This: Example 2B Course 1 10-9 Volume of Cylinders Try This: Example 2B B. Ulysses’ pencil holder 4 in. ÷ 2 = 2 in. Find the radius. V = r2h Write the formula. Replace  with , r with 2, and h with 7. 22 7 __ V   22  7 22 7 __ V = 88 Multiply. The volume of Scott’s pencil holder is about 75 in3.

Course 1 10-9 Volume of Cylinders Additional Example 3A & 3B: Comparing Volumes of Cylinders Find which cylinder has the greater volume. Cylinder 1: V = r2h V  3.14  1.52  12 V  84.78 cm3 Cylinder 2: V = r2h V  3.14  32  6 V  169.56 cm3 Cylinder 2 has the greater volume because 169.56 cm3 > 84.78 cm3.

Find which cylinder has the greater volume. Course 1 10-9 Volume of Cylinders Try This: Example 3A & 3B Find which cylinder has the greater volume. Cylinder 1: V = r2h 10 cm 2.5 cm V  3.14  2.52  10 V  196.25 cm3 4 cm Cylinder 2: V = r2h V  3.14  22  4 V  50.24 cm3 Cylinder 1 has the greater volume because 196.25 cm3 > 50.24 cm3.

Insert Lesson Title Here Course 1 10-9 Volume of Cylinders Insert Lesson Title Here Lesson Quiz Find the volume of each cylinder to the nearest cubic unit. Use 3.14 for . 1. radius = 9 ft, height = 4 ft 1017 ft3 2. radius = 3.2 ft, height = 6 ft 193 ft3 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 cylinder B 1,181.64 ft3 1,560.14 ft3