Volume of Cylinders Notes 10-8 Volume of Cylinders Notes Course 1

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

Additional Example 1A: Finding the Volume of a Cylinder Course 1 10-8 Volume of Cylinders Additional Example 1A: Finding the Volume of a Cylinder Find the volume V of the cylinder to the nearest cubic unit. 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 10-8 Volume of Cylinders Additional Example 1B: Finding the Volume of a Cylinder 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 10-8 Volume of Cylinders Additional Example 1C: Finding the Volume of a Cylinder 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 10-8 Check It Out: Example 1A Course 1 10-8 Volume of Cylinders Check It Out: Example 1A Find the volume V of each cylinder to the nearest cubic unit. 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 10-8 Check It Out: Example 1B 8 cm 6 cm Course 1 10-8 Volume of Cylinders Check It Out: Example 1B 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 10-8 Check It Out: Example 1C h r = + 5 4 h = 8 in Course 1 10-8 Volume of Cylinders Check It Out: Example 1C 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 1,231 in3.

Course 1 10-8 Volume of Cylinders Additional Example 3: 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 10-8 Volume of Cylinders Check It Out: Example 3 Find which cylinder has the greater volume. Cylinder 1: V = r2h 10 cm 2.5 cm 4 cm V  3.14  2.52  10 V  196.25 cm3 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 10-8 Volume of Cylinders Insert Lesson Title Here Lesson Quiz: Part I Find the volume of each cylinder to the nearest cubic unit. Use 3.14 for . 1. radius = 9 ft, height = 4 ft 1,017 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

Insert Lesson Title Here Course 1 10-8 Volume of Cylinders Insert Lesson Title Here Lesson Quiz: Part II 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 396 in2 about 603 in2