Volume of a Cone Using Pappus's Theorem

The video tutorial explains how to use Pappus' theorem to find the volume of a cone formed by rotating a triangle around the y-axis. It covers calculating the area and centroid of the triangle, determining the distance the centroid travels, and verifying the volume using the standard cone volume formula.

What is the shape formed by rotating the given triangle about the y-axis?

• Sphere

• Pyramid

• Cylinder

• Cone

According to Pappus's Theorem, what two components are needed to find the volume of a solid of revolution?

• Area of the base and height

• Area of the region and distance traveled by the centroid

• Radius and height

• Diameter and circumference

How is the area of the triangular region calculated?

• Base plus height

• 1/2 times base times height

• Base times height

• Base minus height

What are the coordinates of the centroid of the triangle?

• (3, 4)

• (0, 0)

• (7/3, 8/3)

• (7, 8)

What is the formula for the distance traveled by the centroid when rotated about the y-axis?

• R^2/2

• R/2

• πR^2

• 2πR

What is the exact volume of the cone calculated using Pappus's Theorem?

• 196 cubic units

• 196 π cubic units

• 392/3 cubic units

• 392/3 π cubic units

What is the radius of the base of the cone?

• 8 units

• 7 units

• 14 units

• 3.5 units

What is the height of the cone?

• 7 units

• 8 units

• 14 units

• 3.5 units

What is the standard formula for the volume of a cone?

• 2/3 πR^2H

• 1/3 πR^2H

• πRH

• πR^2H

How does the volume calculated using Pappus's Theorem compare to the standard cone volume formula?

• It is larger

• It cannot be compared

• It is smaller

• It is the same