Question

The right isosceles triangle shown is rotated about line k with the base forming perpendicular to k. The perimeter of the triangle is 58 units.

An isosceles triangle is rotated about line k on one side. The opposite side has a length of 24 units.

Which best describes the resulting three-dimensional shape?

a cone with a base radius of 17 units
a cone with a base radius of 34 units
a cylinder with a base radius of 17 units
a cylinder with a base radius of 34 units

Answer 1

Let the equal legs each be a. Perimeter: 2a + a√2 = 58 ⇒ a(2+√2) = 58 ⇒ a = 58/(2+√2) ≈ 17. Then the hypotenuse = a√2 ≈ 24 (matches given).

Rotating the right triangle about one leg produces a cone whose base radius is the other leg = 17 units.

Answer: a cone with a base radius of 17 units.