Volume of Solids Problems

This video tutorial covers part two of practice assessments, focusing on the geometry of cylinders, spheres, and cones. It explains how to calculate the volume of a cone using the volume of a cylinder, analyzes the relationship between radius and volume, and demonstrates how to find the volume of a sphere. The tutorial also includes a section on determining the height of a cylinder given its volume and radius, and explores the concept of linear relationships through a volume table.

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

• 26 cubic centimeters

• 39 cubic centimeters

• 78 cubic centimeters

• 52 cubic centimeters

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

• The volume remains the same

• The volume quadruples

• The volume triples

• The volume doubles

What is the formula for the volume of a sphere?

• 4/3 πr³

• 4/3 πr²

• 2/3 πr³

• πr²h

How do you find the height of a cylinder if you know its volume and radius?

• Divide the volume by the radius

• Multiply the volume by the radius

• Divide the volume by πr²

• Multiply the volume by πr²

What is the volume of a cylinder with a radius of 1 and height of 9 in terms of π?

• 27π

• 18π

• 9π

• 36π

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

• It depends on the radius

• Yes, it is linear

• No, it is not linear

• It depends on the height

If a cylinder with a height of 9 inches and radius of 1 fills a pitcher, how many pitchers can a cylinder with a radius of 2 fill?

• 3 pitchers

• 5 pitchers

• 4 pitchers

• 2 pitchers

What happens to the volume of a cylinder if the radius is tripled?

• The volume doubles

• The volume triples

• The volume increases ninefold

• The volume remains the same

What is the volume of a cylinder with a radius of 2 and height of 9 in terms of π?

• 72π

• 54π

• 36π

• 18π

How many times larger is the volume of a cylinder with a radius of 3 compared to one with a radius of 1?

• 12 times larger

• 3 times larger

• 6 times larger

• 9 times larger