Lanier Middle School “An International Baccalaureate Middle Years Programme School” 7th – LESSON 10.2 Volume of Triangular Prisms and Pyramids Daily Objective: How do you find the volume of a triangular prism or a triangular pyramid? If you know the volume and the base area B of a triangular prism, how could you find the height of the prism? Remember that the volume of a prism is given by the formula V B h where B is the base area. Find the volume of a garden seat in the shape of a triangular prism with a height of 30 inches and a base area of 72 square inches. Lets find the volume of the triangular prism. If you have a triangular prism and a triangular pyramid, the volume of the triangular pyramid will be V The volume of a triangular pyramid is 13.5 cubic meters. What is the volume of a triangular prism with a congruent base and the same height? Explain. 1 B h provided 3 both have the same height and congruent bases. How much greater is the volume of a triangular prism with base area of 14 square cm and a height of 4.8 cm than the volume of a triangular pyramid with the same height and base area? Practice 1 Find the volume of the triangular prism. 2 A triangular pyramid and a triangular prism have congruent bases and the same height. The triangular pyramid has a volume of 90m 3 . Find the volume of the prism. 3 In exercise 2, how much greater is the volume of the prism than the volume of the pyramid? Mr. Martinez is building wooden shapes for a sculpture in the park. His plans show a triangular pyramid and a triangular prism, and each shape is 5 feet high. The base of each shape is a triangle with a base of 2.5 feet and a height of 2 feet. How much greater than the volume of the pyramid is the volume of the prism? Lanier Middle School “An International Baccalaureate Middle Years Programme School” Find the volume of each figure. 4 5 7 A pyramid has a base that is a triangle. The length of the triangle is 5 meters, and the height of the triangle is 12 meters. The height of the pyramid is 10 meters. Explain how to find the volume of this pyramid. 6 10 Sandy builds this shape of four congruent triangles using clay and toothpicks. The area of each triangle is 17.6 square centimeters, and the height of the shape is 5.2 cm. What threedimensional figure does the shape Sandy built resemble? If this were a solid shape, what would be its volume? 8 A trap for insects is in the shape of a triangular prism. The area of the base is 3.5 square inches and the height of the prism is 5 inches. What is the volume of this trap? 9 Arletta built a cardboard ramp for her little brothers’ toy cars. Identify the shape of the ramp. Then find its volume. 12 The Jacksons went camping in a state park. One of the tents they took is shown. What is the volume of the tent? 11 Would tripling the height of a triangular prism triple its volume? Explain. 13 Shawntelle is solving a problem involving a triangular pyramid. You hear her say that “bee” is equal to 24 inches. How can you tell if she is talking about the base area B of the pyramid or about the base b of the triangle? 14 Alex made a sketch for a homemade soccer goal he plans to build. The goal will be in the shape of a triangular prism. The legs of the right triangles at the sides of his goal measure 4 feet and 8 feet, and the opening along the front is 24 feet. How much space is contained within this goal? 17 Don and Kayla each draw a triangular pyramid that has a 3 volume of 100 cm . They do not draw identical shapes. Give a set of possible dimensions for each pyramid. 15 A plastic puzzle in the shape of a triangular prism has bases that are equilateral triangles with side lengths of 4 inches and a height of 3.5 inches. The height of the prism is 5 inches. Find the volume of the prism. 16 Lynette’s grandmother has a metal doorstop with the dimensions shown. Find the volume of the metal in the doorstop. The metal in the doorstop has a mas of about 8.6 grams per cubic centimeter. Find the mass of the doorstop. Lanier Middle School “An International Baccalaureate Middle Years Programme School” 18 Don’s favorite cheese snack comes in a box of six pieces. Each piece of cheese has the shape of a triangular prism that is 2 cm high. The triangular base of the prism has a height of 5 cm and a base of 4 cm. Find the volume of cheese in the box. 19 What effect would doubling all the dimensions of a triangular pyramid have on the volume of the pyramid? Explain your reasoning. Use the formula V Bh to find the volume of a gift box that is 3.5 inches high, 7 inches long, and 6 inches wide.
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