Find the volume of the rotating rectangle around an axis if the rectangle is 3ft wide and 10 ft long. The rectangle is 2 ft away from the axis.

Answer 1

5^2pi - 2^2pi = 25pi-4pi = 21pi = the difference of the areas of the bases of two cylinders of radius 5 and 2

V=hA

height = 10 so volume = 210pi = about 659.7339 cubic feet, round off to 660 ft^3

V= 660 ft^3

Or do it as V(5) - V(2) = 250pi - 40pi = 210pi

Answer 2

Imagine a cylinder centred on the axis going out to the outer edge of the rectangle

r = 2 + 3 = 5

h = 10

V = πr²h

Imagine a second cylinder centred on the axis going out to the inner edge of the rectangle

r = 2

h = 10

V = πr²h

Calculate these two volumes and take the smaller from the larger (use π = 3.14)