Understanding the Volume of a Torus

The video tutorial explains how to calculate the volume of a torus formed by rotating a circle around a vertical line. The volume is determined by multiplying the area of the circle by the distance the circle's center travels, which is the circumference of another circle with radius R2. The formula used is pi times the square of R1, the radius of the red circle, times 2 pi R2. By substituting R1 as 3 and R2 as 9, the volume is calculated as 162 pi squared cubic centimeters, approximately 1,598.88 cubic centimeters.

How is the torus formed according to the video?

• By rotating a rectangle around a diagonal line

• By rotating a square around a vertical line

• By rotating a triangle around a horizontal line

• By rotating a circle around a vertical line

What two factors determine the volume of the torus?

• The area of the circle and the height of the torus

• The diameter of the circle and the width of the torus

• The area of the circle and the distance traveled by the circle's center

• The circumference of the circle and the height of the torus

In the volume formula, what does R1 represent?

• The radius of the torus

• The height of the torus

• The radius of the circle

• The distance from the axis to the edge of the torus

What is the role of R2 in the volume formula?

• It is the radius of the circle

• It is the width of the torus

• It is the height of the torus

• It is the distance from the axis of rotation to the center of the circle

What is the exact volume of the torus when R1 is 3 and R2 is 9?

• 324 pi squared cubic centimeters

• 243 pi squared cubic centimeters

• 162 pi squared cubic centimeters

• 81 pi squared cubic centimeters