10.5b Volumes of Pyramids and Prisms

10.5b Volume

Finite Math

EQ: Tuesday, November 29, 2023

• How do I use a basic formula to find the volume of

any prism, pyramids, and cones?

Prisms

a three-dimensional solid object in which the two ends are identical polygons called its bases
Its bases are connected by rectangles called faces.

Prisms are named by the shape of its bases.

Multiple Choice

Which surface is the base of the prism?

​There are 2 identical rectangles connected by rectangles.

Multiple Choice

Which surface is the base of the prism?

​There are 2 identical trapezoids connected by rectangles.

Multiple Choice

Which surface is the base of the prism?

​The volume of a 3-dimensional solid would be like the area of one slice of bread multiplied by the number of slices in the loaf.

​The volume of a prism is the area of its base x the distance between the bases.

Multiple Choice

Find the volume of the triangular prism.

• 185.5 cm3

• 371 cm3

• 378 cm3

• 225.5 cm3

(​area of base)(height)

Math Response

Find the volume of the triangular prism.

Type answer here

Correct Answer: 96

Deg^°

Rad

Find the volume of this prism.

Math Response

Find the volume of the prism. Round your answer to the hundredths place.

Type answer here

Correct Answer: 622.2

Deg^°

Rad

​The volume of a pyramid is one-third of the volume of the box it fits in.

​The volume of a pyramid is one-third of the volume of the box it fits in.

​Basic Volume Formula for Rectangular Pyramids

Math Response

Find the volume of the rectangular pyramid.

Type answer here

Correct Answer: 20

Deg^°

Rad

​Basic Volume Formula for Rectangular Pyramids

Math Response

Find the volume of the pyramid.

Type answer here

Correct Answer: 180

Deg^°

Rad

Find the volume of the rectangular pyramid.

Volume = (⅓)(10m ✕ 6m)(9m)

Volume = 180 cm3

Basic Volume Formula for Cone

Volumecone =1/3 Volumecylinder

Basic Volume Formula for Cone

Volumecone =1/3 Volumecylinder

Basic Volume Formula for Cone

Areacircle = πr2 = π(10m)2

= 100π m2

Volume = (⅓)(100π m2

✕ 20m)

Volumecone =1/3 Volumecylinder

Multiple Choice

Find the volume of the cylinder.

• 2956.25 cm3

• 3619.11 cm3

• 2024.49 cm3

• 2899.61 cm3

Make the things you want to do easy

and the things you
don’t want to do difficult.

Math Response

A 30-foot tall grain silo is 28 feet in diameter. It has a cylindrical side of 25 feet. What is the volume of the silo? Round your answer to a whole number.

Type answer here

Correct Answer: 16412

Deg^°

Rad

Math Response

A 36-foot tall grain silo with a semi-spherical dome top is 40 feet wide. Find the volume of the silo. Round your answer to the nearest whole number.

Type answer here

Correct Answer: 36843

Deg^°

Rad