Volume of 3D Shapes

In this lesson, the teacher covers the final topic of unit 5, focusing on the volumes of cylinders, cones, and spheres. The lesson begins with solving for the radius of a sphere given its volume. The teacher then compares the volumes of different shapes, including a cylinder, cone, rectangular prism, and sphere, to determine which can hold a given volume of water. The lesson emphasizes understanding volume calculations and comparisons across different geometric shapes.

What is the formula for the volume of a sphere?

• V = 1/3 πr²h

• V = πr²h

• V = lwh

• V = 4/3 πr³

If the volume of a sphere is 288π, what is the radius?

• 4

• 5

• 7

• 6

How does the volume of a cone compare to a cylinder with the same dimensions?

• The cone has twice the volume

• The cone has half the volume

• The cone has one-third the volume

• The cone has the same volume

What is the volume of a cylinder with a radius of 1.5 cm and height of 8 cm?

• 24π

• 48π

• 18π

• 36π

Which shape can hold the same volume as a cylinder with a diameter of 6 cm and height of 2 cm?

• A rectangular prism with dimensions 3 cm x 4 cm x 8 cm

• None of the above

• A cone with a radius of 3 cm and height of 8 cm

• A sphere with a radius of 2 cm

What is the volume of a rectangular prism with dimensions 3 cm x 4 cm x 8 cm?

• 144

• 120

• 96

• 72

What is the volume of a sphere with a radius of 2 cm?

• 8π

• 10 2/3π

• 12π

• 14π

Which shape cannot hold the same volume as a cylinder with a diameter of 3 cm and height of 8 cm?

• A cone with a radius of 3 cm and height of 8 cm

• A cylinder with a diameter of 6 cm and height of 2 cm

• A rectangular prism with dimensions 3 cm x 4 cm x 8 cm

• A sphere with a radius of 2 cm

What is the volume of a cylinder with a diameter of 6 cm and height of 2 cm?

• 12π

• 18π

• 24π

• 30π

How do you calculate the volume of a cylinder?

• V = 1/3 πr²h

• V = 4/3 πr³

• V = lwh

• V = πr²h