Finding the Volume of a Sphere using Comparisons with Cylinders

The video tutorial explains how to find the volume of a sphere by comparing it to a cylinder with similar dimensions. It reviews the formula for the volume of a cylinder and derives the formula for the volume of a sphere, which is 4/3 πr³. The tutorial includes examples of applying the formula and highlights common mistakes, such as confusing the formula for surface area with volume.

What is the formula for the volume of a cylinder with a circular base?

• V = 4/3 pi r cubed

• V = pi r squared

• V = 2 pi r cubed

• V = pi r squared h

How many hemispheres are needed to fill a cylinder with the same radius and height?

• Three

• One

• Four

• Two

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

• 2/3 pi r cubed

• 4 pi r squared

• 4/3 pi r cubed

• pi r squared h

If a sphere has a radius of 3 cm, what is its volume in terms of pi?

• 36 pi cm cubed

• 18 pi cm cubed

• 27 pi cm cubed

• 32/3 pi cm cubed

What is a common mistake when calculating the volume of a sphere?

• Using the formula for a rectangle

• Using the formula for surface area

• Using the formula for a cylinder

• Using the formula for a cone