Lesson 7-1 Volume of Cylinders Page 79 Determine the volume of the cylinder. Round to the nearest tenth. V Bh V (π r ) h Volume of a cylinder The base is a circle. V π() (5) Replace r with and h with 5. V 11. in Mia s parents have a cylindrical oak tree stump that has a diameter of feet and a height of feet. How much does the stump weigh if the average weight of oak is 59 pounds per cubic foot? Round to the nearest tenth. First find the volume of the stump. V Bh V (π r ) h Volume of a cylinder The base is a circle. V π(1.5) () Replace r with 1.5 and h with. V 1.1 ft Simplif y. To find the weight of the stump, multiply the volume by 59. 1.1(59) = 81.9 So, the weight of the stump is about 81.9 pounds. Texas Math, Course
Lesson 7- Volume of Cones Pages 91-9 Determine the volume of a cone with a height of 8. feet and a diameter of.5 feet. Round to the nearest tenth. 1 π V r h V 1 π(1.75) (8.) Volume of a cone Replace r with 1.75 and h with 8.. V 6.9 ft A cylinder has a radius of 5 centimeters and a height of 1 centimeters. What would the height of a cone need to be if it has the same volume and radius? Round to the nearest centimeter. Let h be the height of the cylinder, H be the height of the cone, and r be the radius of both. 1 πr h π r H 1 π(5) (1) π(5) H 1 00π = (5)π H 900π = 5π H The volume of the cylinder is equal to the volume of the cone. Replace r with 5 and h with 1. Multiply both sides by. 900π 5π = H 5π 5π Divide each side by 5π. 6 H Simplif y. The height of the cone is 6 centimeters. Texas Math, Course
Lesson 7- Volume of Spheres Page 99 Determine the volume of the sphere. Round to the nearest tenth. V π r V π(7.) Volume of a sphere Replace r with 7.. V 1,56. 5 in Use a calculator. The radius of a basketball is.7 inches. What is the volume of the basketball? Round to the nearest tenth. V π r Volume of a sphere V π(.7) V Replace r with.7.. 9 Use a calculator. The volume of the basketball is about.9 cubic inches. Texas Math, Course
Lesson 7- Surface Area of Prisms Page 515 1 Determine the lateral and surface area of the rectangular prism. Round to the nearest tenth if necessary. Determine the lateral area. L.A. = Ph Lateral area of a rectangular prism L.A. = (9 + 5 + 9 + 5)8 Replace P with the perimeter of the base and h with 8. L.A. = The lateral area is square centimeters. Determine the surface area. S = Ph + B Surface area of a rectangular prism S = + (9 5) Replace Ph with and B with the area of the base. S = 1 The surface area is 1 square centimeters. When making a book cover, Anwar uses enough material to cover the front, back, and spine of the book. He adds 0 square inches more to the surface area to allow for overlap. How many square inches of paper will Anwar use to make a book cover for a book 11 inches long, 8 inches wide, and 1 inch high? Determine the surface area of the book Anwar needs to cover by finding the surface area of the front, back, and spine of the book. Then add 0 square inches. The surface area of the front, back, and spine is (11)(8) + (11)(8) + (11)(1) or 187 square inches. So, Anwar will use 187 + 0 or 07 square inches of paper to make the book cover. Texas Math, Course
Lesson 7-5 Surface Area of Cylinders Page 55 Determine the total surface area of the cylinder. Round to the nearest tenth. S πrh π r S π()(5) π() S 88.0 mm Surface area of a cylinder Replace r with and h with 5. Determine the lateral area of a cylindrical copper pipe that has a diameter of 6. inches and a height of 1 inches. Round to the nearest tenth. L. A. π rh LA.. π(.)(1) Lateral area of a cylinder Replace r with. and h with 1. L. A. 1. The lateral area of the pipe is about 1. square inches. Texas Math, Course
Lesson 7-6 Changes in Dimensions Pages 55-56 A cereal box has a surface area of 80 square inches. What is the surface area of a similar box with dimensions that are larger by a scale factor of 1.? SA.. 80 1. SA.. 80 1.96 SA.. 58.8 Multiply by the square of the scale factor. Square 1.. The surface area of the larger box is 58.8 square inches. Use a Problem-Solving Model Two spheres are similar in shape. The scale factor between the smaller sphere and the larger sphere is. If the volume of the smaller sphere is 16.9 cubic meters, what is the volume of the larger sphere? The scale factor between the larger sphere and the smaller sphere is. V 16.9 Multiply by the cube of the scale factor. 6 V 16.9 7 Cube. V 00.8 The volume of the larger sphere is 00.8 cubic meters. Texas Math, Course