A triangle has sides that measure 15 cm, 36 cm, and 39 cm.

Question

A triangle has sides that measure 15 cm, 36 cm, and 39 cm. Find the exact volume (in cubic centimeters) of the solid of revolution formed when the triangle is revolved about the side of length 15 cm. (Hint: The triangle is a right triangle.)

Answer 1

When a triangle is revolved about one of its sides, the 3D shape formed is a cone with a circular base, with a radius equal to the base of the triangle (with a question like this, it may benefit to draw a visual to really understand the dimensions of the shape).

Thus, the radius is 36 cm.

Now the side that is staying in place that the shape is revolving around becomes the height since it makes a right angle with the base of the cone.

Thus, the height is 15 cm.

All there's left to do is to plug into the formula.

The formula for the volume of a right circular cone is V = (1/3)πr²h

Then, V = (1/3) π (36)² (15)

Thus, the volume is 6,480π cm³ (since volume is always expressed in cubic units)