Lesson 3: Definition and Properties of Volume for Prisms and Cylinders
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1 : Definition and Properties of Volume for Prisms and Cylinders Learning Targets I can describe the properties of volume. I can find the volume of any prism and cylinder using the formula Area of Base Height. Volume Properties Definition: Volume is the that a three-dimensional figure can occupy. Ex: The volume of a glass is the amount of liquid it can hold. For any right rectangular or triangular prism, the formula of the volume is as follows: For any Cylinder the volume is given by the following formula V = (Area of Base) Height = BH V Rect = V = V = (Area of Base) Height = BH V = Example 1. Find the volume of each solid shape A. B.
2 C. Find the volume of the triangular prism shown D. Find the volume of the triangular prism Look at the solids below. Are the two volumes different? Why? By Cavalieri s principle, if two solids have equal and equal parallel areas at every height, then the volumes of the two solids would be. Example 2. Determine the volume of the rectangular prism shown at right in in. Example 3. An oblique circular cylinder has height 5 and volume of 45π. Find the radius of the circular base in.
3 Composite Volumes Example 6. Find the volume. Example 7. A 3" hole is drilled through a solid cylinder with a diameter of 4" forming a tube. What is the volume of the tube? Example 8. Find the volume of the composite figure. Example 9. Determine whether Cavalieri s Principle can be used to compare the volumes of any of the solids. Explain your reasoning.
4 : Definition and Properties of Volume for Prisms and Cylinders Classwork 1. Find the volume of each rectangular prism a. b. 2. Find the volume of the triangular prism a. b. 3. Find the volume of the following solid 4. The radius of the base of a cylinder is 39 in. and its height is 33 in. Find the volume of the cylinder.
5 5. A cylinder has a volume of cubic inches and a base diameter of 12 in. Find the height of the cylinder. 6. Find the volume of the cylinder. 7. Denise wants to use a cylindrical garbage can for recycling. The can has a diameter of 4 feet and a height of 2.5 feet. How many cubic feet of recycling will fit into the garbage can? 8. A washer is a cylindrical solid with a smaller cylinder removed from the center. The diameter of the washer is 3, the diameter of the hole is ½, and height ¼. Find the volume of the washer. 9. Find the volume of the composite figure.
6 Lesson 5: Definition and Properties of Volume for Prisms and Cylinders Homework 1. A packing carton in the shape of a triangular prism is shown in the diagram at right. What is the volume, in cubic inches, of this carton? 1) 20 2) 60 3) 120 4) Tim has a rectangular prism with a length of 10 centimeters, a width of 2 centimeters, and an unknown height. He needs to build another rectangular prism with a length of 5 centimeters and the same height as the original prism. The volume of the two prisms will be the same. Find the width, in centimeters, of the new prism. 3. Two prisms with equal altitudes have equal volumes. The base of one prism is a square with a side length of 5 inches. The base of the second prism is a rectangle with a side length of 10 inches. Determine and state, in inches, the measure of the width of the rectangle. 4. Which expression represents the volume, in cubic centimeters, of the cylinder represented in the diagram below? 1) 2) 3) 4)
7 5. A cylinder has a height of 7 cm and a base with a diameter of 10 cm. Determine the volume, in cubic centimeters, of the cylinder in terms of. 6. A right circular cylinder has a volume of 1,000 cubic inches and a height of 8 inches. What is the radius of the cylinder to the nearest tenth of an inch? 1) 6.3 2) ) )
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