Cylinder and Cone Volume Problems

This video tutorial covers part two of practice assessments, focusing on geometric shapes like cylinders, spheres, and cones. It explains how to calculate the volume of a cone using the volume of a cylinder, analyze the relationship between radius and volume, and calculate the volume of a sphere. The tutorial also demonstrates how to find the height of a cylinder given its volume and radius, and explores the concept of linear relationships in volume tables.

What is the volume of a cone if a cylinder with the same radius and height has a volume of 78 cubic centimeters?

• 39 cubic centimeters

• 78 cubic centimeters

• 52 cubic centimeters

• 26 cubic centimeters

If the radius of a cone doubles, how does the volume change?

• It doubles

• It triples

• It quadruples

• It remains the same

What is the approximate volume of a sphere with a radius of 2.7 cm?

• 100 cubic centimeters

• 50 cubic centimeters

• 30 cubic centimeters

• 82 cubic centimeters

Given a cylinder with a radius of 1.6 meters and a volume of 95 cubic meters, what is its height?

• 13.2 meters

• 11.8 meters

• 10.5 meters

• 8.0 meters

For a cylinder with a height of 9 inches and a radius of 1, what is the volume in terms of pi?

• 9 pi

• 6 pi

• 3 pi

• 12 pi

If the radius of a cylinder is increased from 1 to 2, how does the volume change?

• It remains the same

• It doubles

• It triples

• It quadruples

What is the volume of a cylinder with a radius of 3 and height of 9 in terms of pi?

• 54 pi

• 27 pi

• 81 pi

• 108 pi

Is the relationship between the radius and volume of a cylinder linear?

• Yes, it is linear

• No, it is not linear

• It depends on the radius

• It depends on the height

How many times larger is the volume of a cylinder with a radius of 2 compared to one with a radius of 1?

• 4 times

• 5 times

• 3 times

• 2 times

If a cylinder with a radius of 1 fills a pitcher, how many pitchers can a cylinder with a radius of 2 fill?

• 3 pitchers

• 1 pitcher

• 2 pitchers

• 4 pitchers