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FINDING VOLUME Volume measures the amount a solid figure can hold. Volume is measured in terms of units³ and can be measured in inches, feet, meters, centimeters, and millimeters. • The formula for the volume of a rectangular prism is V = l · w · h, where l is the length, w is the width, and h is the height. • The formula for the volume of a cube is V = s³, where s is a side of the square. • The volume of a triangular prism is V = (1/2) · l · w · h . • The volume of a cylinder is V = π r² · h, where r is the radius and h is the height. Pi is usually 3.14. • The volume of a pyramid is V = (1/3) b² · h , where b is the side of the base and h is the height of the pyramid. • The volume of a cone is V = (1/3)π r² · h, where r is the radius and h is the height. • The volume of a sphere is V = (4/3)π r³, w here r is the radius and π is 3.14. • The figures of prisms, cylinders, pyramids, cones and spheres are all 3-D figures. The 3-D figures are made up of edges, faces and vertices. The edge is where two faces meet. The face is the side of the figure. The vertex is the point where the edges meet. © Copyright NewPath Learning. All Rights Reserved. Permission is granted for the purchaser to print copies for non-commercial educational purposes only. Visit us at www.NewPathLearning.com.

How to use finding volume The volume of 3-D figures can be determined by using the formula that corresponds to the figure. The volumes of all figures can be determined as long as the needed information is given. • For example, what is the volume of a cone with a radius of 6 cm and a height of 15 cm? Ex. Vcone = (1/3)π r² · h = (1/3)(3.14)(6²)(15) Vcone = (1/3)(3.14)(36)(15) = 565.2 cm³ If the volume of a figure is given, as well as the information needed to solve for volume except one value, the missing value can be found by substituting in all the given information and solving. • For example, if the volume of a sphere is 33.49 m, what is the radius of the sphere? Ex. Vsphere = (4/3)π r³ 33.49 = (4/3)(3.14)r³ 33.49 = 4.187r³ 4.187 4.187 7.999 = r³ r³ ≈ 8, r ≈ 2 because 2 · 2 · 2 =8 The radius of the sphere is approximately 2 m. A 3-D figure is made up of faces, edges and vertices. A rectangular prism has 6 faces, 12 edges and 8 vertices. © Copyright NewPath Learning. All Rights Reserved. Permission is granted for the purchaser to print copies for non-commercial educational purposes only. Visit us at www.NewPathLearning.com.

Try This! 1. What is the volume of the rectangular prism with a length of 3m, a width of 5 m and a height of 11m? V = l · w · h 2. What is the volume of a triangular prism with a length of 6 cm, a width of 7 cm and a height of 2 cm? V = (1/2) · l · w · h 3. What is the volume of a cylinder with a radius of 4 ft and a height of 9 ft? V = π r² · h 4. What is the volume of a pyramid with a height of 12 cm and a base of 4 cm? V = (1/3) b² · h 5. What is the volume of a cone with a radius of 5 in. and a height of 18 in.? V = (1/3)π r² · h 6. What is the volume of a sphere with a radius of 27 cm and a height of 33cm? V = (4/3)π r³ 7. If the volume of a rectangular prism is 288 cm³ and the length is 9 cm and the width is 8 cm, what is the height? V = l · w · h 8. If the volume of a triangular prism is 81 ft³ and the width is 6 ft and the height is 3 ft, what is the length? V = (1/2) · l · w · h 9. If the volume of a cylinder is 1230.88 m³ and the radius is 7 m, what is the height? V = π r² · h © Copyright NewPath Learning. All Rights Reserved. Permission is granted for the purchaser to print copies for non-commercial educational purposes only. Visit us at www.NewPathLearning.com.

10. If the volume of a pyramid is 125cm³ and the height is 15 cm, what is the radius? V = (1/3) b² · h 11. If the volume of a cone is 1780.38 in.³ and the radius is 9 in., what is the height? V = (1/3)π r² · h 12. If the volume of a sphere is 113.04ft, what is the radius? V = (4/3)π r³ 13. How many faces does a pyramid have? 14. How many edges does a triangular prism have? 15. How many vertices does a rectangular prism have? © Copyright NewPath Learning. All Rights Reserved. Permission is granted for the purchaser to print copies for non-commercial educational purposes only. Visit us at www.NewPathLearning.com.