Geometry of Pyramids and Frustums

The video tutorial explains how to calculate the volume of a frustum, which is a truncated pyramid. The process involves finding the volume of the entire pyramid and subtracting the volume of the removed top section. The tutorial covers setting up proportions to determine dimensions, applying the Pythagorean theorem to find heights, and using volume formulas for both the full and truncated pyramids. The final volume is calculated by subtracting the smaller pyramid's volume from the larger one.

What is a frustum in geometry?

• A complete pyramid

• A cone with a circular base

• A pyramid with the top cut off

• A cylinder with a square base

Tags

CCSS.HSG.GMD.A.3

How do you find the volume of a frustum?

• By subtracting the volume of the smaller pyramid from the larger one

• By dividing the base area by the height

• By adding the volumes of two pyramids

• By multiplying the base area by the height

Tags

CCSS.HSG.GMD.A.3

What is the formula for the volume of a pyramid?

• 1/2 base area times height

• 1/3 base area times height

• Base area times height

• Base area divided by height

Tags

CCSS.7.G.B.6

What is the base area of the larger pyramid in the example?

• 36

• 49

• 100

• 64

Tags

CCSS.7.G.A.1

How is the height of the larger pyramid determined?

• By guessing

• Using proportions and the Pythagorean theorem

• By measuring directly

• Using the area of the base

Tags

CCSS.HSG.GMD.A.3

What is the length of the full edge of the larger pyramid?

• 18

• 20

• 15

• 12

Tags

CCSS.HSG.GMD.A.3

What is the height of the smaller pyramid?

• 18.7

• 11.2

• 20

• 15.5

Tags

CCSS.7.G.B.6

What is the base area of the smaller pyramid?

• 64

• 100

• 36

• 49

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

What is the final volume of the frustum?

• 500.5

• 488.9

• 134.4

• 623.3

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

What is the unit of the final volume of the frustum?

• Cubic inches

• Square inches

• Square feet

• Cubic feet

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3