Question

The lengths of the legs of a right triangle are 4 cm and 6 cm. If the triangle is rotated about one of its legs to create a right
circular cone, find the volume of the cone of greatest volume. Round to the nearest tenth. Show your work (4 points)

Answer 1

If you rotate about the leg of length 4 then the radius of the base of the cone is 6 and the height is 4.
Volume of a cone is V=1/3*pi*r^2*h
V=1/3*pi*6^2*4
=1/3*pi*36*4
=pi*48
=150.8 cm^3

To make sure that is the greatest volume we can figure the other cone.
If you rotate around the leg of length 6 your radius will be 4 and your height will be 6.
V=1/3*pi*4^2*6
V=100.5 cm^3