Sphere Geometry and Calculations

The video tutorial focuses on solving backwards problems by using given information to find unknowns. It starts with calculating the radius and diameter of a sphere from its area using the formula 4πr². The process involves dividing the area by 4π and taking the square root to find the radius, then doubling it for the diameter. Next, the tutorial explains how to calculate the volume of the sphere using the formula 4/3πr³. The video concludes with a summary of the process and introduces word problems, emphasizing the importance of working from area to linear measurements and then to volume.

What is the first step in solving backward problems involving spheres?

• Find the volume directly.

• Guess the radius and check.

• Calculate the diameter first.

• Use the given area to find the radius.

Which formula is used to find the radius from the area of a sphere?

• 4 π r^2

• 4/3 π r^3

• 2 π r

• π r^2

If a sphere has an area of 24 square inches, what is the approximate radius?

• 1.91 inches

• 1.38 inches

• 3.14 inches

• 2.76 inches

Which mathematical operation is used to find the radius from R squared?

• Division

• Multiplication

• Square root

• Cube root

What is the constant value of π used in calculations?

• 3.142

• 3.1415

• 3.14159

• 3.14

How do you calculate the diameter of a sphere once you have the radius?

• Divide the radius by 2.

• Add 2 to the radius.

• Multiply the radius by 4.

• Multiply the radius by 2.

What is the diameter of a sphere with a radius of 1.38 inches?

• 4.00 inches

• 1.38 inches

• 2.76 inches

• 3.14 inches

What is the formula for the volume of a sphere?

• 4/3 π r^3

• 2 π r

• π r^2 h

• 4 π r^2

What is the volume of a sphere with a radius of 1.38 inches?

• 10.00 cubic inches

• 11.01 cubic inches

• 9.00 cubic inches

• 12.00 cubic inches

What is the key approach in solving backward problems involving spheres?

• Use the diameter to find the area.

• Guess the measurements and verify.

• Work from area to linear measurements, then to volume.

• Start with the volume and find the area.