Volume of Spheres and Cylinders

This lesson covers the volume of a sphere, starting with a review of volume formulas for various shapes. The teacher explains how the volume of a sphere is derived from the volume of a cylinder and provides the formula: four-thirds times pi times the radius cubed. The lesson includes several examples and practice problems to reinforce understanding, emphasizing the importance of memorizing the formula. The session concludes with a summary of the key points covered.

What is the main objective of today's lesson?

• To calculate the surface area of a cylinder.

• To understand the properties of a rectangular prism.

• To apply the formula for the volume of a sphere to real-world problems.

• To learn the formula for the volume of a cube.

How is the volume of a sphere related to the volume of a cylinder?

• A sphere's volume is equal to a cylinder's volume.

• A sphere's volume is two-thirds of a cylinder's volume.

• A sphere's volume is double a cylinder's volume.

• A sphere's volume is half of a cylinder's volume.

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

• 2/3 × π × radius cubed

• 4/3 × π × radius squared

• 4/3 × π × radius cubed

• π × radius squared × height

In the first example, what is the radius of the sphere used?

• 3 cm

• 4 cm

• 6 cm

• 5 cm

What is the volume of a sphere with a radius of 4 cm?

• 267.9 cm³

• 300 cm³

• 150 cm³

• 200 cm³

In the second example, what is the radius of the sphere?

• 7 cm

• 6 cm

• 5 cm

• 8 cm

What is the volume of a sphere with a radius of 6 cm?

• 700 cm³

• 800 cm³

• 904.32 cm³

• 678.24 cm³

What is the radius of the largest sphere that can fit inside a cylinder with a height of 14 inches?

• 7 inches

• 6 inches

• 9 inches

• 8 inches

What is the volume of a sphere with a radius of 7 inches?

• 1500.00 inches³

• 1000.02 inches³

• 1200.50 inches³

• 1436.02 inches³

What is the formula used to find the volume of a sphere?

• 2/3 × π × radius cubed

• π × diameter cubed

• 4/3 × π × radius cubed

• π × radius squared × height