University:
Bradley University
Course:
MTH 119 | Calculus With Review B
Academic year:

2022
Views:

431

Pages:

7
Author:

Remington Spence

Applications with the Volume of a Cylinder Warm-Up ? Lesson Question How can you apply the formula for the volume of a cylinder to solve problems? Lesson Goals Apply the volume formula for a cylinder. Calculate unknown measures W 2K Solve real-world of a cylinder. problems . Words to Know Fill in this table as you work through the lesson. You may also use the glossary to help you. cylinder a solid figure with two congruent circular or elliptical bases connected to a curved side radius a segment that extends from the center of a circle to any point on the circle volume the measure of the amount of space occupied by a three-dimensional solid object approximate near or very close to the actual 1 Warm-Up Applications with the Volume of a Cylinder Determining Volume Given Radius and Height Follow the steps to find the volume. 1. Substitute the known measures for the corresponding 2. Simplify to find the volume variables . . 5 ft 3 ft What is the volume of a cylinder with a radius of 5 feet and a height of 3 feet? • Cylinder V = Bh V = πr 2h V = π(52)( 3 ) V = π(25)(3) = 75π V = 75π ft 3 Remember that B represents the area of the base of the figure. 2 Instruction Applications with the Volume of a Cylinder Slide 2 Calculating Unknown Measures PROCEDURE volume 1. Apply the formula for the of a cylinder. 2. Substitute the known measures for the corresponding variables in the formula. 3. Apply the properties of equality to solve for the variable. What is the area of the base of a cylinder with a volume of 240π cm3 and a height of 12 cm? Cylinder V = Bh V = Bh 240π = 12 20π B(12) cm2 = B The area of the base is 20π cm2. 3 12 Instruction Applications with the Volume of a Cylinder Slide 5 Applying the Formula to Calculate Height EXAMPLE What is the height of a cylinder with a volume of 162π in.3 and a radius of 6 inches? Cylinder V = Bh Solve for h. V = πr 2 ⋅ h 2 162π = 162π = π( 36 ) 4.5 Check: π(6 ) ⋅ ( h ) π(36) ⋅ h π(36) in. = h 162π = π(62 )(4.5) 162π = 162π The height of a cylinder with a volume of 162π in.3 and a radius of 6 inches is 4.5 inches. 4 Instruction Applications with the Volume of a Cylinder Slide 2 Determining How Much Water a Cylinder Will Hold REAL-WORLD CONNECTION Swimming pools are often in the shape of a cylinder. The height of this pool is 5 feet. The radius of the pool is 20 feet. Approximately how much water will completely fill the pool? V = Bh V = πr 2 ⋅ h • Cylinder V = Bh 20 ft 5 ft V = π(202)( V = π( V = 400 5 ) )(5) 2000π Use a calculator to find an approximate answer to the nearest hundredth. V≈ 6,283.19 5 ft3 Instruction Applications with the Volume of a Cylinder Slide 5 Finding the Base Area EXAMPLE This swimming pool can hold approximately 6,283.19 cubic feet. The inside bottom of the pool is covered with decorative tile. What is the approximate area of the tile design on the bottom of the pool? • Cylinder V = Bh 5 ft V = Bh 6,283.19 = B(5) 6,283.19 B(5) = 5 5 1,256.64 = B B≈ 1,256.64 ft2 The approximate area of the tile design on the bottom of the pool is 1,256.64 ft2. 6 Summary ? Lesson Question Applications with the Volume of a Cylinder How can you apply the formula for the volume of a cylinder to solve problems? Answer Applying the formula can help determine the area of the base or height of a cylindrical shape by using substitution and the properties of equality. Use this space to write any questions or thoughts about this lesson. 7