The volume V of a cylinder is of the area of the base and the height. Algebra V= πr^2h. Also, this pdf includes Comparing Volumes of Cylinders and Standardized Test Practice.
1. N SO Volume of Cylinders LES Goal: Find the volume of cylinders. Volume of a Cylinder Words The volume V of a cylinder is the product of r the area of the base and the height . h Algebra V πr 2h EXAMPLE 1 Standardized Test Practice What is the volume of the cylinder? Use 3.14 for π. 4m You have learned 5m many properties and formulas related to solids. Writing a summary of what you A 62.8 m3 B 251.2 m3 have learned may help C 314 m3 D 1256 m3 you prepare for the chapter test. Solution V πr 2h Write formula for volume of a cylinder. Substitute 3.14 for π, 4 for r, 3.14 (4)2 5 and 5 for h. 251.2 Multiply. Answer: The volume of the cylinder is about 251.2 cubic meters . The correct answer is B . A B C D 274 | Chapter 12 Notetaking Guide
2. EXAMPLE 2 Comparing Volumes of Cylinders Tomato Sauce Carlos found two cans of tomato sauce in the pantry. One can has a diameter of 4 inches and a height of 5 inches. The second one has a diameter of 3 inches and a height of 6 inches. Which can has the greater volume? Solution WATCH OUT! 1. Find the radius of each can, which is 4 in. 3 in. Make sure to use the half of the diameter. radius, not the diameter, in the formula for 4 Can 1: r 2 2 in. 5 in. 6 in. volume of a cylinder. 3 Can 2: r 2 1.5 in. 2. Find the volume of each can. Use 3.14 for π. Can 1: Can 2: V πr h 2 V πr 2h 3.14 (2)2 5 3.14 (1.5)2 6 62.8 in.3 42.39 in.3 Answer: Can 1 has the greater volume. EXAMPLE 3 Finding the Radius of a Cylinder A cylinder has a height of 12 feet and a volume of 3768 cubic feet. Find the radius of the cylinder. Use 3.14 for π. V πr 2h Write formula for volume of a cylinder. Need Substitute 3768 for V, 3.14 for π, help with solving 3768 3.14 r 2 12 equations using and 12 for h. square roots? See page 579 of your 3768 37.68r 2 Multiply. textbook. 100 r 2 Divide each side by 37.68 . r 100 Take positive square root of each side. 10 r Evaluate square root. Answer: The radius of the cylinder is about 10 feet . Lesson 12.6 Volume of Cylinders | 275
3. Guided Practice Find the volume of the cylinder. Use 3.14 for π. 1. 2. 6 in. 3. 8m 2 cm 1 cm 9 in. 6m 12.56 cm3 1017.36 in.3 301.44 m3 4. Find the radius of a cylinder that has a height of 7 inches and a volume of 351.68 cubic inches. Use 3.14 of π. 4 in. 276 | Chapter 12 Notetaking Guide