Learn how to determine the volume of a sphere

The video tutorial explains the concept of a great circle on a sphere, using the Earth as an example. It describes how a great circle is the largest possible circle that can be drawn on a sphere, dividing it into two equal hemispheres. The tutorial then demonstrates how to calculate the radius of a sphere using the area of a great circle and subsequently find the surface area of the sphere. The process involves using the formula for the area of a circle (πR²) and the surface area formula for a sphere (4πR²).

What is a great circle on a sphere?

• A circle that divides the sphere into two equal halves

• A circle that is perpendicular to the sphere's diameter

• A circle with a smaller diameter than the sphere

• A circle that is tangent to the sphere

How is the Earth divided into hemispheres?

• By using the Tropic of Cancer

• By cutting along the prime meridian

• By using the equator as a great circle

• By cutting along the International Date Line

What formula is used to find the area of a great circle?

• πD

• 4πR²

• πR²

• 2πR

How do you calculate the radius of a sphere from the area of a great circle?

• Multiply the area by 2 and take the square root

• Multiply the area by π and take the square root

• Divide the area by π and take the square root

• Divide the area by 2π and take the square root

What is the formula for the surface area of a sphere?

• 2πR²

• 4πR²

• πR²

• 3πR²

If the radius of a sphere is 3 inches, what is its surface area?

• 27π square inches

• 9π square inches

• 12π square inches

• 36π square inches

What is the surface area of a sphere with a great circle area of 28.6 square inches?

• 113.1 square inches

• 90.2 square inches

• 100.5 square inches

• 120.3 square inches