Volume and Surface Area of Solids

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 calculate the volume of a sphere. The tutorial also includes solving for the height of a cylinder given its volume and radius, creating a volume table, and addressing complex volume-related questions. The session emphasizes understanding key geometric relationships and applying algebraic techniques.

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

• 26 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 doubles

• The volume triples

• The volume quadruples

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

• No, it is not linear

• Yes, it is linear

• It depends on the radius

• It depends on the height

What is the volume of a sphere with a radius of 2.7 cm, rounded to the nearest cubic centimeter?

• 100 cubic centimeters

• 82 cubic centimeters

• 50 cubic centimeters

• 30 cubic centimeters

What is the formula for the volume of a sphere?

• pi r^2 h

• 4/3 pi r^2

• pi r^3

• 4/3 pi r^3

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

• 20.0 meters

• 8.0 meters

• 11.8 meters

• 15.0 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

• 18 pi

• 27 pi

• 36 pi

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

• Twice as large

• Five times as large

• Three times as large

• Four times as large

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

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

• 4 pitchers

• 3 pitchers

• 2 pitchers

• 5 pitchers