Volume and Surface Area of Solids

This video tutorial covers part two of practice assessments, focusing on geometric shapes such as 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 through graphing, and demonstrates how to calculate the volume of a sphere. Additionally, it includes a section on finding 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?

• 78 cubic centimeters

• 52 cubic centimeters

• 39 cubic centimeters

• 26 cubic centimeters

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

• The volume doubles

• The volume remains the same

• The volume triples

• The volume quadruples

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

• Yes, it is linear

• No, it is not 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?

• 30 cubic centimeters

• 50 cubic centimeters

• 82 cubic centimeters

• 100 cubic centimeters

What is the formula for the volume of a sphere?

• 4/3 pi r^3

• pi r^2 h

• 4/3 pi r^2

• pi r^3

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

• 11.8 meters

• 8.0 meters

• 13.2 meters

• 10.5 meters

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

• 12 pi

• 9 pi

• 3 pi

• 6 pi

How many times larger is the volume of a cylinder when its radius is doubled?

• Four times as large

• Five times as large

• Twice as large

• Three times as large

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

• 72 pi

• 18 pi

• 36 pi

• 54 pi

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

• 2 pitchers

• 3 pitchers

• 5 pitchers

• 4 pitchers