Volume and Surface Area of Solids

The 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, analyze graph relationships 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, create a volume table, and solve a complex volume question involving cylinders. Key concepts include understanding geometric relationships and applying formulas for volume calculations.

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

• 52 cubic centimeters

• 78 cubic centimeters

• 26 cubic centimeters

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

• 82 cubic centimeters

• 100 cubic centimeters

• 50 cubic centimeters

• 30 cubic centimeters

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

• 8.0 meters

• 11.8 meters

• 10.5 meters

• 13.2 meters

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

• 36π

• 27π

• 18π

• 9π

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

• It doubles

• It remains the same

• It triples

• It quadruples

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

• 27π

• 108π

• 54π

• 81π

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

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

• 3 times

• 5 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?

• 1 pitcher

• 2 pitchers

• 3 pitchers

• 4 pitchers