Calculating the Volume of a Pyramid

This video tutorial by Mr. J explains how to find the volume of a pyramid using two formulas: one-third times the area of the base times the height, and the area of the base times the height divided by three. The video provides two examples: one with a square base and another with a rectangular base. It also explains why the pyramid's volume is one-third of a prism with the same base and height, enhancing understanding of the formula.

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

• Volume = 1/3 * Base Area * Height

• Volume = Base Area * Height

• Volume = Base Area + Height

• Volume = 1/2 * Base Area * Height

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CCSS.HSG.GMD.A.3

Can the volume formula for pyramids be applied regardless of the base shape?

• Yes, but only for triangular bases.

• No, only for rectangular bases.

• Yes, for any base shape.

• No, only for square bases.

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CCSS.HSG.GMD.A.3

How do you calculate the area of a square base for volume calculation?

• Area = Length + Width

• Area = Length * Width

• Area = Side^2

• Area = 2 * Side

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CCSS.6.G.A.2

CCSS.5.MD.C.5B

What is the area of a square base if one side is 6 inches?

• 24 square inches

• 12 square inches

• 36 square inches

• 18 square inches

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CCSS.4.MD.A.3

CCSS.3.MD.C.7B

What is the volume of a pyramid with a square base of side 6 inches and height 4 inches?

• 72 cubic inches

• 48 cubic inches

• 144 cubic inches

• 96 cubic inches

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CCSS.HSG.GMD.A.3

Is multiplying by 1/3 the same as dividing by 3 in the context of pyramid volume calculation?

• Yes, they are equivalent.

• Only when the base is a square.

• No, they produce different results.

• Only when the base is a triangle.

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CCSS.HSG.GMD.A.3

Why is the volume of a pyramid one-third the volume of a prism with the same base and height?

• Because it has 1/3 the height of the prism.

• Because it occupies 1/3 the space within the prism.

• Because it has 1/3 the base area of the prism.

• Because it is a more complex shape.

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CCSS.HSG.GMD.A.3

What is the purpose of dividing by 3 or multiplying by 1/3 in the pyramid volume formula?

• To adjust for the pyramid's slant height.

• To convert from square units to cubic units.

• To account for the pyramid occupying 1/3 the space of a prism with the same base and height.

• To simplify the calculation process.

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CCSS.HSG.GMD.A.3

How do you calculate the area of a rectangular base for volume calculation?

• Area = 2 * (Length + Width)

• Area = Length + Width

• Area = Length * Width

• Area = Length^2 + Width^2

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CCSS.6.G.A.2

CCSS.5.MD.C.5B

What is the volume of a pyramid with a rectangular base of length 8 meters and width 7 meters, and height 11 meters?

• 924 cubic meters

• 308 cubic meters

• 205.33 cubic meters

• 616 cubic meters

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CCSS.HSG.GMD.A.3