Volume and Properties of Spheres

This video tutorial explains how to calculate the volume of a sphere using the formula 4/3 πr³. It begins with an introduction to the concept of volume and focuses on spheres. The tutorial then explains how to derive the radius from a given diameter, cube the radius, and apply the formula to find the volume. The video also demonstrates the calculation process, including using the commutative property and estimating the final result. The tutorial emphasizes the importance of using a calculator for precise results and provides a step-by-step guide to solving the problem manually.

What is the main focus of the video tutorial?

• Understanding the volume of a sphere

• Learning about the circumference of a circle

• Calculating the surface area of a cube

• Finding the area of a circle

What is the formula for the volume of a sphere?

• 2 π r^3

• 4/3 π r^2

• 4/3 π r^3

• π r^2 h

If the diameter of a sphere is 10 inches, what is the radius?

• 15 inches

• 10 inches

• 20 inches

• 5 inches

How do you calculate the radius cubed?

• Multiply the radius by 2

• Square the radius

• Multiply the radius by itself three times

• Add the radius three times

What is the result of cubing a radius of 5 inches?

• 75

• 15

• 125

• 25

What property is used to rearrange the multiplication in the formula?

• Commutative Property

• Distributive Property

• Associative Property

• Identity Property

What is the mixed number form of 500 divided by 3?

• 166 and 1/3

• 166 and 2/3

• 167 and 1/3

• 167 and 2/3

Why is it recommended to use a calculator for this calculation?

• To avoid using pi

• To simplify the formula

• To handle complex decimals

• To skip the calculation

What is the approximate value of pi used in the calculation?

• 3.14

• 3.16

• 3.15

• 3.13

What is the final volume of the sphere rounded to the nearest hundredths place?

• 422.31 inches cubed

• 423.31 inches cubed

• 420.31 inches cubed

• 425.31 inches cubed