Volume and Surface Area of Solids

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, analyzes the relationship between radius and volume, and demonstrates how to calculate the volume of a sphere. The tutorial also includes a section on finding the height of a cylinder given its volume and radius, and discusses the creation of a volume table to explore linear relationships.

What geometric shapes are discussed in Part Two of the practice assessments?

• Hexagons and octagons

• Rectangles and triangles

• Cubes and pyramids

• Cylinders, spheres, and cones

What is the key relationship between the volume of a cylinder and a cone with the same height and radius?

• The cone's volume is equal to the cylinder's

• The cone's volume is double the cylinder's

• The cone's volume is one-third of the cylinder's

• The cone's volume is half of the cylinder's

If a cylinder has a volume of 78 cubic centimeters, what is the volume of a cone with the same dimensions?

• 52 cubic centimeters

• 39 cubic centimeters

• 26 cubic centimeters

• 78 cubic centimeters

What does the graph show about the relationship between the radius and volume of cones?

• It is a quadratic relationship

• It is a linear relationship

• It is not a linear relationship

• It is a constant relationship

If the radius of a cone doubles, what happens to its volume?

• The volume triples

• The volume quadruples

• The volume doubles

• The volume remains the same

What is the formula for calculating the volume of a sphere?

• 4/3 πr²

• 4/3 πr³

• πr²h

• 2/3 πr³

Calculate the volume of a sphere with a radius of 2.7 cm to the nearest cubic centimeter.

• 30 cm³

• 100 cm³

• 50 cm³

• 82 cm³

What is the formula for the volume of a cylinder?

• πr³

• 2πr²h

• πr²h

• 4/3 πr³

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

• 13.4 meters

• 11.8 meters

• 8.5 meters

• 10.2 meters

In the volume table, what is the volume of a cylinder with a radius of 2 and height of 9?

• 18π

• 36π

• 54π

• 72π