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Math-8 NOTES DATE: ______/_______/_______ What: applying Volume... Why: To investigate a variety of different types of volume applications, including real- life scenarios for volume. What: applying Volume... Why: To investigate a variety of different types of volume applications, including real- life scenarios for volume. NAME: Changing an attribute: What are attributes ? If we double one attribute of a prism, the volume will also ____________________________? If we triple one __________________________________ of a prism, the volume will also _________________________________. If we multiply one attribute of a prism by any number, the volume will increase by that number! If we multiply one attribute by a fraction, the volume will _______________________________________ by that fraction. What about surface area ? ScenarioAnswer 1)The volume of a certain Fed-Ex box is 64 in.³ If the height were tripled, what would the new volume be? 2)One prism has a length of 15 cm., a width of 12 cm., and a height of 6 cm., so its volume is 1,080 cm.³ If its width were changed to 4 cm., what would the new volume be? Key words for volume problems:

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4)Study the below prism. If the height of the prism is increased to 15 cm., and the other dimensions remain the same, what happens to the volume? Solving for a missing dimension: Sometimes a word problem will give us the volume or surface area already, BUT will ask us to solve for a missing dimension– like length, width, or ________________________________. We can use the formulas to help us. Let’s try some volume examples: ScenarioAnswer 1)The volume of a circular pool is 251.2 ft.³ If the radius of the pool is 4 ft., what is the depth (height)? 3) A sandbox is 4 ft. long, 3 ft. wide, and 2 ft. tall. Another sandbox is 8 ft. long, 3 ft. wide, and 2 ft. tall. Compare the volume of the smaller sandbox to the volume of the larger sandbox.

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3)The volume of a square-based pyramid is 15 un.³ On the square base, the side length is 3 un. What is the height of the pyramid? 4)An ice cream cone holds 94.2 cm.³ of ice cream. If the radius is 3 cm., what is the height? 5)The volume of a triangular prism is 36 un.³ If the triangle faces have a base length of 3 un. and a height of 4 un., what is the height of entire prism? 2)A rectangular planter box holds 144 in.³ of dirt. If its length is 12 in. and its width is 4 in., what is its height?

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NAME: ____________________________DATE: ______/_______/_______ Miscellaneous Volume ScenariosAnswer 1)Gary is pouring concrete into a rectangular mold. If the mold is 3 ft. long, 2 ft. tall, and 4.5 ft. wide, how much concrete will the mold hold? 2)A tuna fish can holds approximately 628 cm³ of tuna fish. If the radius is 5 cm., what is the height? 3)A triangular prism has a volume of 80 in.³ If the height is decreased by ¼, what will the new volume be? 4)In order to fill a glass to the brim, how much tea will Larry have to pour if the diameter of the glass is 5 cm. and the height is 12 cm.? 5)Mary keeps her swimming ribbons in a rectangular box that is 10 inches long, 2.5 inches wide, and 3 inches tall. She buys a new ribbon box that has the same length and width, but the height is 6 inches. What is the volume of the new ribbon box? 6)A sand bucket for building sand castles is in the shape of a square-based pyramid. If the side length of the base is 8.5 in. and the height of the pyramid is 10 in., how much sand can the pyramid bucket hold? 7)The volume of a square-based pyramid is 144 cm.³ A cube has the same base and the same height. What is the volume of the cube? (Hint: Think of the water demonstration that we did in class.)

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Miscellaneous Volume ScenariosAnswer 8)How much ice cream can a cone with a radius of 1.5 in. and a height of 5 in. hold? 9)A triangle-based pyramid has a triangle base-length of 4 cm. long and is 3 cm. in height. If the entire pyramid is 10.5 cm. tall, what is the volume? 10) A cylinder has a volume of 288 un³. If the radius is 6 in., what is the approximate height? 11) One sandbox holds 6 ft.³ of sand. A larger sandbox holds 24 ft.³ of sand. If the length and width of both sandboxes are equal, and the height of the smaller sandbox is 1 ft., then what is the height of the larger sandbox? 12) A cylinder-shaped glass can hold 24 un³. A cone has a circle-base that is congruent to the base of the glass. The height of the cone and glass are also congruent. What is the volume of the cone? (Hint: Again, think of the water demonstration we did in class.)

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