Exploring Surface Area and Volume of Pyramids

The video tutorial covers the surface area and volume of pyramids, comparing them to prisms. It explains how to draw and label the net of a pyramid, including calculating the slant height using the Pythagorean theorem. The tutorial then demonstrates how to calculate the surface area and volume of the pyramid, emphasizing the importance of understanding the base area and lateral area. The video concludes with a practical example of how a pyramid's volume relates to a prism with the same base and height.

What distinguishes a pyramid from a prism?

• A pyramid cannot have a square base, but a prism can.

• A pyramid and a prism are essentially the same.

• A pyramid has two bases, while a prism has only one.

• A pyramid has only one base, while a prism has two.

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CCSS.2.G.A.1

CCSS.1.G.A.1

What shape forms the base of the pyramid discussed?

• Circle

• Triangle

• Rectangle

• Square

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CCSS.7.G.A.3

What theorem is used to calculate the slant height of the pyramid?

• Pythagorean Theorem

• Fermat's Last Theorem

• Euclidean Theorem

• Thales' Theorem

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CCSS.8.G.B.7

What is the length of the slant height of the pyramid?

• 5 units

• 10 units

• 13 units

• 12 units

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CCSS.7.G.B.6

How do you calculate the area of a triangle on the pyramid's net?

• Base times height

• Base plus height

• Base times height divided by 2

• Base plus height divided by 2

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CCSS.6.G.A.4

What is the total surface area of the pyramid?

• 100 units squared

• 260 units squared

• 400 units squared

• 360 units squared

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CCSS.7.G.B.6

What is the area of the base of the pyramid?

• 130 units squared

• 120 units squared

• 100 units squared

• 140 units squared

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CCSS.7.G.B.6

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

• Area of the base times height divided by 3

• Area of the base plus height divided by 3

• Area of the base times height divided by 2

• Area of the base times height

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CCSS.HSG.GMD.A.3

How many pyramids fit into a prism with the same base area and height?

• Five

• Four

• Three

• Two

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CCSS.HSG.GMD.A.3

What is the volume of the pyramid?

• 300 units cubed

• 400 units cubed

• 500 units cubed

• 600 units cubed

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CCSS.HSG.GMD.A.3