Exploring Volumes of Prisms and Cylinders

This video tutorial covers the calculation of volumes for prisms and cylinders. It begins with an introduction to the formula for volume, which is the area of the base times the height. The video provides examples of calculating the volume of rectangular and triangular prisms, as well as cylinders. It also explains how to find the volume of composite solids by breaking them into simpler shapes. The tutorial emphasizes understanding the geometric properties and applying the correct formulas to find volumes.

What is the formula to calculate the volume of a prism?

• Volume = Base Area - Height

• Volume = (Base Area x Height) / 2

• Volume = Base Area x Height

• Volume = Base Area + Height

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CCSS.7.G.B.6

How do you find the volume of a rectangular prism with a base area of 24 square units and height of 10 units?

• 480 cubic units

• 240 cubic units

• 2400 cubic units

• 4800 cubic units

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CCSS.7.G.B.6

What special right triangle is used to find the height in the triangular prism example?

• 90-90-90 triangle

• 45-45-90 triangle

• 30-60-90 triangle

• 60-60-60 triangle

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CCSS.7.G.B.6

What is the volume of a triangular prism with a base area of 30 square units and a height of 5 units?

• 75 cubic units

• 300 cubic units

• 60 cubic units

• 150 cubic units

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CCSS.7.G.B.6

How is the volume of a cylinder calculated?

• Volume = πr + h

• Volume = πr^2 + h

• Volume = πr^2h

• Volume = 2πrh

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CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

What is the volume of a cylinder with a radius of 3 units and height of 8 units, in terms of π?

• 24π cubic units

• 72π cubic units

• 64π cubic units

• 96π cubic units

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CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

Does an oblique cylinder have the same volume as a right cylinder with the same base and height?

• Yes

• Only if the height is greater than the radius

• No

• Only if the height is less than the radius

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CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

How do you calculate the volume of a composite solid?

• By multiplying the volumes of its parts

• By subtracting the volumes of its parts

• By dividing the volume of the larger part by the smaller

• By adding the volumes of its parts

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CCSS.5.MD.C.5C

What is the volume of the bottom piece of the composite solid if its base area is 48 square units and height is 2 units?

• 96 cubic units

• 46 cubic units

• 24 cubic units

• 192 cubic units

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CCSS.7.G.B.6

What is the total volume of the composite solid discussed in the video?

• 144 cubic units

• 240 cubic units

• 192 cubic units

• 288 cubic units

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CCSS.5.MD.C.5C