Volume of a Sphere

This video tutorial covers how to find the volume of a sphere and its relationship to a cylinder. It explains the formula for the volume of a sphere, demonstrates calculations with examples, and discusses how to find the radius when given the volume. The lesson also includes a comparison of the volumes of spheres and cylinders, and how to calculate the volume of a hemisphere.

What is one of the main objectives of this lesson?

• To find the surface area of a sphere

• To understand the relationship between the volume of a sphere and a cylinder

• To calculate the perimeter of a circle

• To learn about the history of geometry

How is a sphere defined?

• A flat surface extending infinitely in all directions

• A two-dimensional shape with equal sides

• A three-dimensional figure where each point on the surface is equidistant from the center

• A shape with four equal sides and angles

What is the formula for the volume of a sphere?

• 4/3 × π × r³

• π × d

• π × r² × h

• 2/3 × π × r²

How do you find the volume of a hemisphere?

• Multiply the volume of a sphere by 2

• Divide the volume of a sphere by 2

• Multiply the radius by 3

• Use a special formula different from a sphere

What is the relationship between the volume of a sphere and a cylinder with the same radius and height?

• The sphere's volume is twice the cylinder's volume

• The sphere's volume is 2/3 of the cylinder's volume

• The sphere's volume is equal to the cylinder's volume

• The sphere's volume is 1/3 of the cylinder's volume

If a sphere has a radius of 6 inches, what is its volume using π as 3.14?

• 452.16 cubic inches

• 904.32 cubic inches

• 113.04 cubic inches

• 678.24 cubic inches

What is the volume of a sphere with a diameter of 14 inches using π as 3.14?

• 1,200 cubic inches

• 1,436 cubic inches

• 2,000 cubic inches

• 1,000 cubic inches

How do you calculate the volume of a hemisphere with a radius of 8 inches?

• Use the sphere volume formula and add 10

• Use the sphere volume formula and divide by 2

• Use the sphere volume formula and multiply by 2

• Use the sphere volume formula and subtract 5

What is the first step in finding the radius of a sphere when given the volume?

• Subtract π from the volume

• Add the volume to π

• Divide the volume by π

• Multiply the volume by π

If the volume of a sphere is given as 256/3 π, what is the radius?

• 3 inches

• 5 inches

• 6 inches

• 4 inches