Holt CA Course Volume of Cylinders MG1.3 Know and use the formulas for the volume of triangular prisms and cylinders (area of base × height); compare these formulas and explain the similarity between them and the formula for the volume of a rectangular solid. Also covered: AF3.1, AF3.2 California Standards

Holt CA Course 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. V = Bh The area of the circular base is r 2. V = r 2 h

Holt CA 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 352 ft 3.

Holt CA 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 864 cm 3. Find the volume V of the cylinder to the nearest cubic unit.

Holt CA 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 1,385 in 3. Find the volume V of the cylinder to the nearest cubic unit.

Holt CA Course Volume of Cylinders Check It Out! Example 1A Find the volume V of the 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

Holt CA 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 6. V = r 2 h V  3.14  4 2  6 Find the volume V of the cylinder to the nearest cubic unit.

Holt CA Course Volume of Cylinders 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 Find the volume V of the cylinder to the nearest cubic unit.

Holt CA Course 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. 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

Holt CA Course Volume of Cylinders 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 __

Holt CA Course Volume of Cylinders 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

Holt CA Course Volume of Cylinders 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

Holt CA Course Volume of Cylinders 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.

Holt CA Course Volume of Cylinders 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 cm 2.5 cm 4 cm