Calculating Volumes of Prisms and Pyramids

This video tutorial explains how to calculate the volume of prisms and pyramids. It covers the formulas for finding the volume of rectangular and triangular prisms, as well as rectangular and triangular pyramids. The tutorial provides step-by-step examples, highlighting the importance of identifying the base area and height for each shape. For prisms, the volume is calculated by multiplying the base area by the height, while for pyramids, the formula includes a one-third factor. The video emphasizes understanding the geometric properties of each shape to apply the correct formula.

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

• V = (1/3) x base area x height

• V = (base area x height) / 2

• V = base area x height

• V = length x width x height

Tags

CCSS.7.G.B.6

If a rectangular prism has a base area of 33 mm² and a height of 9 mm, what is its volume?

• 342 mm³

• 102 mm³

• 99 mm³

• 297 mm³

Tags

CCSS.7.G.B.6

How do you find the area of the base in a triangular prism?

• 2 x Base x Height

• (1/3) x Base x Height

• Base x Height / 2

• Base x Height

Tags

CCSS.7.G.B.6

What is the volume of a triangular prism with a base area of 24 m² and a height of 10 m?

• 240 m³

• 60 m³

• 120 m³

• 480 m³

Tags

CCSS.7.G.B.6

Which of the following is a correct step in calculating the volume of a prism?

• Divide the base area by 2

• Divide the base area by the height

• Multiply the base area by the height

• Multiply the base area by 1/3

Tags

CCSS.7.G.B.6

What modification is made to the volume formula when calculating the volume of a pyramid?

• Multiply by 1/2

• Multiply by 1/3

• Divide by 1/2

• Divide by 1/3

Tags

CCSS.HSG.GMD.A.3

If a rectangular pyramid has a base area of 21 cm² and a height of 12 cm, what is its volume?

• 336 cm³

• 63 cm³

• 252 cm³

• 84 cm³

Tags

CCSS.HSG.GMD.A.3

In the context of pyramids, why is the volume formula multiplied by 1/3?

• Because it's a mathematical convention without physical meaning

• To simplify the calculation process

• To account for the triangular base

• Because a pyramid has 1/3 the volume of a prism with the same base area and height

Tags

CCSS.HSG.GMD.A.3

To find the area of a triangular base, you multiply the base by the height and then divide by what number?

• 1

• 2

• 3

• 4

Tags

CCSS.6.G.A.1

What is the volume of a triangular pyramid with a base area of 150 inches² and a height of 21 inches?

• 750 inches³

• 1050 inches³

• 3150 inches³

• 525 inches³

Tags

CCSS.HSG.GMD.A.3