Volume of Cones and Cylinders

The video tutorial explains how to design a storage building for fertilizer with a cylindrical base and a cone-shaped top. The building must adhere to specific dimensions, with a maximum width of 8 feet and a height of 14 feet. The tutorial calculates the volume of fertilizer delivered by dump trucks and demonstrates how to design the storage to accommodate this volume. It explores different height combinations for the cylinder and cone to ensure the storage can hold the required amount of fertilizer.

What is the shape of the base of the storage building?

• Pyramidal

• Spherical

• Cylindrical

• Rectangular

What is the maximum width allowed for the storage building?

• 8 feet

• 12 feet

• 6 feet

• 10 feet

How many dump truck loads of fertilizer need to be stored?

• Two

• One

• Three

• Four

What is the formula for the volume of a cylinder?

• pi r squared times height

• 1/3 pi r squared times height

• 2 pi r squared times height

• pi r cubed

What is the formula for the volume of a cone?

• pi r cubed

• 1/3 pi r squared times height

• 2 pi r squared times height

• pi r squared times height

What is the radius of the storage building if the maximum width is 8 feet?

• 3 feet

• 4 feet

• 2 feet

• 5 feet

What is the total maximum height allowed for the storage building?

• 16 feet

• 10 feet

• 14 feet

• 12 feet

If the cone's height is 3 feet, what is the height of the cylinder?

• 9 feet

• 10 feet

• 11 feet

• 12 feet

What is the total volume of the storage building with a cone height of 3 feet and a cylinder height of 11 feet?

• 500.16 cubic feet

• 603.16 cubic feet

• 700.16 cubic feet

• 800.16 cubic feet

Does the calculated volume of 603.16 cubic feet exceed the required 576 cubic feet?

• Yes

• No

• Exactly equal

• Not enough information