Volumes of Pyramids, Cones, and Spheres Lessons

Multiple Choice

There are many cylinders with a height of 18 meters. Let $$r$$ represent the radius in meters and $$V$$ represent the volume in cubic meters. Which equation represents the volume $$V$$ as a function of the radius $$r$$ ?

• V = 18rπ
• V = 9πr²
• V = 36πr
• V = 18πr²

Multiple Choice

What is the volume $$V$$ in cubic meters of a cylinder with a radius of 1 meter and a height of 18 meters?

• 72.00
• 30.00
• 45.00
• 56.55

Open Ended

There are many cylinders with a height of 18 meters. Let $$r$$ represent the radius in meters and $$V$$ represent the volume in cubic meters. If the radius of a cylinder is doubled, does the volume double? Explain how you know.

Open Ended

There are many cylinders with a height of 18 meters. Let $$r$$ represent the radius in meters and $$V$$ represent the volume in cubic meters. Is the graph of this function a line? Explain how you know.

Multiple Choice

What is the volume of a cone with a radius of 3 units and a height of 4 units?

• 12π
• 15π
• 9π
• 6π

Open Ended

Another cone has quadruple the radius and the same height. How many times larger is the new cone’s volume? Explain how you know.

Multiple Choice

A cylinder has a radius of 4 cm and a height of 5 cm. What is the volume of the cylinder?

• 60π cm³
• 100 cm³
• 40π cm³
• 80π cm³ or approximately 251.2 cm³

Multiple Choice

A cylinder has a radius of 4 cm and a height of 5 cm. What is the volume of the cylinder when its radius is tripled?

• 240π cm³
• 60π cm³
• 720π cm³
• 480π cm³

Multiple Choice

A cylinder has a radius of 4 cm and a height of 5 cm. What is the volume of the cylinder when its radius is halved?

• 15π cm³
• 10π cm³
• 30π cm³
• 20π cm³

Multiple Choice

A cone has a volume $$V$$ , radius $$r$$ , and a height of 12 cm. A cone has the same height and $$\frac13$$ of the radius of the original cone. What is the expression for its volume?

• (4/9) * π * r^2
• (2/3) * π * r^2
• (1/3) * π * r^2
• (1/2) * π * r^2