Calculating Surface Area and Volume of Pyramids

This video tutorial explains how to calculate the surface area and volume of pyramids. It begins with an introduction to the concepts, followed by a detailed explanation of finding the surface area of a square-based pyramid. The tutorial demonstrates using the Pythagorean theorem to determine the height of the lateral face when the height of the pyramid is given. Finally, it covers the formula for calculating the volume of a pyramid using the base area and the height of the pyramid.

What do we call the bottom part of a pyramid?

• Apex

• Lateral face

• Base

• Vertex

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CCSS.1.G.A.1

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How do you calculate the area of the base for a square-based pyramid?

• Length x Width

• Length + Width

• Base x Height / 2

• Base x Height

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CCSS.7.G.B.6

What formula is used to calculate the area of a triangular lateral face?

• Base x Height

• Base x Height / 2

• (Base x Height) / 3

• Length x Width

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CCSS.7.G.B.6

How many lateral faces does a square-based pyramid have?

• 2

• 3

• 4

• 5

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CCSS.1.G.A.1

CCSS.2.G.A.1

How do you find the height of a lateral face when only the pyramid's height is given?

• Using the Pythagorean theorem

• Multiplying the base by the height of the pyramid

• Adding the base to the height of the pyramid

• Dividing the pyramid's height by 2

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What is the significance of the Pythagorean theorem in calculating the surface area of a pyramid?

• It is used to find the height of the lateral faces

• It is used to calculate the volume

• It helps in finding the base area

• It calculates the slant height

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CCSS.7.G.B.6

Why can't the height of the pyramid be used directly to find the area of the lateral faces?

• Because it does not reach the base

• Because it does not provide the necessary measurement for area calculation

• Because it is only relevant for volume calculation

• Because it is not perpendicular to the base

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CCSS.7.G.B.6

What is the total surface area of a pyramid with a base area of 64 cm² and lateral faces area of 128.96 cm²?

• 192.96 cm²

• 256 cm²

• 128.96 cm²

• 64 cm²

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CCSS.7.G.B.6

What is the formula for calculating the volume of a pyramid?

• Base Area + Height

• (Base Area x Height) / 2

• Base Area x Height

• (Base Area x Height) / 3

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CCSS.HSG.GMD.A.3

What is the role of dividing by 3 in the formula for calculating the volume of a pyramid?

• It adjusts for the pyramid's slant height

• It accounts for the pyramid having one-third the volume of a prism with the same base area and height

• It compensates for the base area being a square

• It reflects the pyramid's three-dimensional shape

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