STAAR Category 3 Grade 7 Mathematics TEKS 7.8A/7.9A. Student Activity 1. Problem 1: The height of a prism is the distance between the two.
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1 Student Activity 1 Work with your partner to answer the following questions. Problem 1: The height of a prism is the distance between the two. The height of a pyramid is the distance from the vertex the base to the. A triangular pyramid and triangular prism have congruent bases and heights. The ratio of the volume of a triangular pyramid to the volume of a triangular prism is to. The formula for the volume of a prism is V Bh. V represents the of the prism. The B represents the of the base of the. The h represents the of the prism. When square inches are multiplied with inches, the units become inches. Problem 2: A triangular prism has a base area of 36 square inches and a height of 12 inches. What is the volume of the prism? Using V Bh, V = ( ) ( ) = cubic inches If a pyramid has the same base and height as the prism, the volume of the pyramid would be divided by. The volume of the pyramid is cubic inches. Problem 3: A triangular pyramid has a volume of 60 cubic feet. The volume of a prism with the same base and height as the pyramid would be 3. The volume of the prism is cubic feet. Is it possible the pyramid and prism have a triangular base with a base of 6 feet and a height of 3 feet, and the height of the pyramid and prism is 10 feet? Explain Is it possible the pyramid and prism have a height of 6 feet and a right triangular base with leg lengths of 15 feet and 4 feet? Explain. TEKSING TOWARD STAAR 2014 Page 1
2 Problem 4: A triangular pyramid and prism have congruent bases and heights. Billy calculated the volume of the prism to be 54 cubic units. John calculated the volume of the pyramid to be 16 cubic units. Is it possible they are both correct in their calculations? Explain your answer. Problem 5: The triangle below represents the base of a triangular prism and triangular pyramid. Using your STAAR rulers, measure the dimensions of the base to the nearest centimeter. Label your measurements on the sketch. The height of both the prism and the pyramid is 14 centimeters. What is the area of the base of the figures? square centimeters What is the volume of the prism? cubic centimeters What is the volume of the pyramid? cubic centimeters What is the ratio of the volume of the pyramid to the volume of the prism? TEKSING TOWARD STAAR 2014 Page 2
3 Student Activity 2 Work with your partner to answer the following questions. Problem 1: Write three formulas that can be used when solving problems involving the volume of a triangular prism. Write three formulas that can be used when solving problems involving the volume of a triangular pyramid. Write the formula you could use to find the area of the base of a triangular prism or pyramid. Problem 2: A model of a triangular pyramid is shown below. The height of the pyramid is 10 inches. 8 in. 6 in. What is the volume of the pyramid? 1. The area of the base is 1 = square inches The height of the pyramid is inches. 3. The formula for the volume of a pyramid is. Substituting for the area of the base and for the height, the volume will be 1 = 3 cubic inches. Problem 3: The model of a triangular prism is shown below. The area of the base of the prism is 20 square units and the volume of the prism is 300 cubic units. What is the height of the prism? TEKSING TOWARD STAAR 2014 Page 3
4 Problem 4: A triangular prism has a volume of 540 cubic units. What is the volume of a triangular pyramid that has the same base and height as the prism? Problem 5: The triangular prism shown below has a right triangle base. The legs of the triangle are 10 units each. The volume of the prism is 1,125 cubic units. What is the area of the base of the prism? Show your work and any formulas you use. What is the height of the prism? Show your work and any formulas you use. Problem 6: The volume of a triangular prism is 1500 cubic units. The height of the prism is 25 units. What is the area of the base of the prism? 1. The formula that has B isolated is B =. 2. Substitute for V and for h. 3. Simplify the expression. B =. What is the label for B? Problem 7: The volume of a triangular pyramid is 500 cubic units. The height of the pyramid is 10 units. What is the area of the base of the pyramid? 1. The formula that has B isolated is B =. 2. Substitute for V and for h. 3. Simplify the expression. B =. What is the label for B? TEKSING TOWARD STAAR 2014 Page 4
5 Problem 8: Which has the larger volume? A. Rectangular prism with a length of 6 centimeters, a width of 10 centimeters, and a height of 5 centimeters B. Triangular prism with a height of 9 units and a triangular base whose height is 8 units and whose base is 10 units. The prism has the larger volume by cubic centimeters. Problem 9: Which figure below has the larger volume? 14 in. 6 in. 11 in. 10 in. 10 in. 8 in. Prism A Prism B The base area of Prism A is 1 ( )( ) or square inches. 2 The height of Prism A is inches. The volume of Prism A is ( ) ( ) or cubic inches. The base area of Prism B is 1 ( )( ) or square inches. 2 The height of Prism B is inches. The volume of Prism B is ( ) ( ) or cubic inches. Prism has the greater volume by cubic inches. TEKSING TOWARD STAAR 2014 Page 5
6 NAME DATE SCORE /5 7.8A/7.9A Skills and Concepts Homework 1 1. A triangular prism and a triangular pyramid have congruent bases and heights. The volume of the prism is 174 cubic units. What is the volume of the pyramid? 2. A triangular prism and a triangular pyramid have congruent bases and heights. The prism s triangular base has a height of 12 centimeters and a base of 8 centimeters. It has a volume of 720 cubic centimeters. What are the volume and the height of the pyramid? 3. A triangular prism and a triangular pyramid have congruent bases and heights. What is the ratio of the volume of the prism to the volume of the pyramid? 4. A triangular prism and a triangular pyramid have congruent bases and heights. The pyramid has a volume of 1,008 cubic units. The triangular base of the pyramid is shown below. What is the height of the prism and pyramid? 18 units 24 units 5. A triangular prism and a triangular pyramid have congruent bases and heights. The prism has a volume of 1,512 cubic units. The triangular base of the prism is shown below. What are the volume and the height of the pyramid? 12 units 28 units TEKSING TOWARD STAAR 2014 Page 6
7 NAME DATE SCORE /5 7.8A/7.9A Skills and Concepts Homework 2 1. A triangular prism has a volume of 540 cubic units. The height of the prism is 18 units. What is the area of the base of the prism? The area of the base is square units. 2. A triangular prism has a height of 12 centimeters. The base of the prism is an equilateral triangle with a base of 8 centimeters and a height of 6.9 centimeters. What is the volume of the prism? 3. A triangular pyramid has a volume of 300 cubic inches. Its height is 10 inches. The base is a right triangle. Give two sets of possible lengths of the legs of the right triangle. 4. A triangular prism has a base area of 20 square inches and a height of 5 inches. What is the volume of the prism when it is filled to 75% capacity? 5. Compare the volume of a triangular pyramid that is 12 inches tall and a base area of 5 square inches and the volume of a triangular prism that is 8 inches tall and the base is a right triangle whose legs are 6 inches and 2 inches. TEKSING TOWARD STAAR 2014 Page 7
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