Lesson 4.6 Core Focus on Geometry Volume of Cylinders

Warm-Up Find the area of each circle. Use 3.14 for . 1. 2. 3. Which has a larger area, a square with side lengths that are 10 units or a circle with a diameter of 10 units? 13 cm ≈ 530.66 cm2 21 cm ≈ 346.185 cm2 the square

Lesson 4.6 Volume of Cylinders Find the volume of cylinders and solve real-world problems involving cylinders.

Vocabulary Volume The number of cubic units needed to fill a three-dimensional figure. Cylinder A solid with two congruent and parallel bases that are circles.

V = Bh V = πr2h B Volume of a Cylinder The volume of a cylinder is equal to the product of the area of the base (B) and the height (h). V = Bh V = πr2h r h B

Example 1 8 m 5 m Find the volume of the cylinder. Use 3.14 for π. Write the volume formula for a cylinder. V = πr2h Substitute all known values for the variables. V ≈ (3.14)(8)2(5) Find the value of the power. V ≈ (3.14)(64)(5) Multiply. V ≈ 1004.8 The volume of the cylinder is about 1,004.8 cubic meters.

Good to Know! The missing dimension of a cylinder can be found if the volume and one other measurement is provided. 1. Substitute all known values into the volume formula. 2. Use inverse operations to find the missing value.

Example 2 The volume of cylindrical water cooler is 1,695.6 cubic inches. The cooler has a radius of 6 inches. Find the height of the cooler. Use 3.14 for π. Write the formula for a cylinder. Substitute all known values for the variables. Find the value of the power. Multiply. Divide both sides of the equation by 113.04. The height of the water cooler is about 15 inches. V = πr2h (1695.6) ≈ (3.14)(6)2h 1695.6 ≈ (3.14)(36)h 1695.6 ≈ 113.04h 113.04 113.04 15 ≈ h

Only the positive root is appropriate in this situation. Example 3 Find the radius of a cylinder with an approximate volume of 3,014.4 cubic inches and a height of 15 inches. Use 3.14 for π. Write the volume formula for a cylinder. Substitute known values for the variables. Multiply. Divide both sides of the equation by 47.1. Square root both sides of the equation. Simplify. The radius of the cylinder is about 8 inches. V = πr2h (3014.4) ≈ (3.14)(r 2)(15) 3014.4 ≈ 47.1r 2 47.1 47.1 64 ≈ r 2 Only the positive root is appropriate in this situation.

Communication Prompt Explain how to find the radius of a cylinder if you know its height and its volume.

Exit Problems 1. Find the volume of the cylinder. Use 3.14 for . 2. A cylindrical cookie jar has a volume of 904.23 cubic inches. It is 8 inches tall. What is the radius of the cookie jar? 30 m 24 m ≈ 16,956 cubic meters 6 inches