Exploring Surface Area and Volume of Spheres

The video tutorial explains the concepts of surface area and volume of spheres. It begins by defining a sphere as a set of points equidistant from a center point, and describes the properties of radius and diameter. The tutorial also covers cross sections and great circles, providing formulas for calculating the surface area and volume of a sphere. An example using a standard bowling ball is provided to demonstrate these calculations, emphasizing the use of a calculator for precise results.

What is the fixed point in the space from which all points on a sphere are equidistant called?

• Diameter

• Circumference

• Center

• Radius

What term describes a line segment from the center of the sphere to any point on its surface?

• Circumference

• Diameter

• Radius

• Arc

What is the term for the line segment passing through the center of the sphere with endpoints on the sphere?

• Circumference

• Arc

• Radius

• Diameter

What do you call a cross-section of a sphere that shares the same center as the sphere?

• Small circle

• Great circle

• Minor circle

• Major circle

What shape is formed when a sphere is cut by a plane?

• Triangle

• Rectangle

• Square

• Circle

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

• 2πr²

• πr²

• 4πr²

• 2πr³

How do you calculate the volume of a sphere?

• 2πr³/3

• πr³/3

• 4πr²/3

• 4πr³/3

If the diameter of a sphere is 8.5 inches, what is the radius?

• 8.5 inches

• 17 inches

• 4.25 inches

• 12.75 inches

Using the formula 4πr², what is the surface area of a sphere with a radius of 4.25 inches?

• 227 square inches

• 200 square inches

• 250 square inches

• 300 square inches

What is the volume of a sphere with a radius of 4.25 inches using the formula 4πr³/3?

• 321 cubic inches

• 350 cubic inches

• 300 cubic inches

• 400 cubic inches