3D Figures and Volume Formulas

This video tutorial teaches how to calculate the volume of three 3D figures: a cylinder, a cone, and a sphere. It begins with the formula for a cylinder, which involves finding the area of the circular base and multiplying it by the height. The tutorial then explains that the volume of a cone is one-third that of a cylinder with the same base and height. Finally, it covers the volume of a sphere, which is two-thirds the volume of a cylinder with the same radius and a height of twice the radius. Each section includes examples to illustrate the calculations.

What are the three 3D figures discussed in this lesson?

• Cube, Pyramid, Cylinder

• Pyramid, Sphere, Cylinder

• Cylinder, Cone, Sphere

• Sphere, Cube, Cone

What is the formula for the area of a circle used in calculating the volume of a cylinder?

• 2 times Radius

• Pi times Diameter

• Pi times Radius squared

• Length times Width

If the radius of a cylinder is 2 inches, what is the base area?

• 16 Pi

• 4 Pi

• 2 Pi

• 8 Pi

What is the volume of a cylinder with a radius of 2 inches and height of 5 inches?

• 30 Pi inches cubed

• 10 Pi inches cubed

• 20 Pi inches cubed

• 40 Pi inches cubed

What is the formula for the volume of a cylinder?

• 1/3 Pi R squared times H

• 4/3 Pi R cubed

• 2 Pi R squared times H

• Pi R squared times H

What is the base area of a cylinder with a radius of 2 inches?

• 16 Pi

• 4 Pi

• 2 Pi

• 8 Pi

What is the volume of a cylinder with a radius of 3 inches and height of 5 inches?

• 75 Pi inches cubed

• 30 Pi inches cubed

• 45 Pi inches cubed

• 60 Pi inches cubed

How is the volume of a cone related to the volume of a cylinder with the same base and height?

• It is equal to the volume of the cylinder

• It is half the volume of the cylinder

• It is twice the volume of the cylinder

• It is one-third the volume of the cylinder

What is the formula for the volume of a cone?

• Pi R cubed

• 2/3 Pi R squared times H

• Pi R squared times H

• 1/3 Pi R squared times H

How does the base area of a cone change as the height increases?

• It decreases

• It doubles

• It increases

• It remains constant