Question

A right cone has a slant height of 20 feet, and the diameter of the base is 24 feet. What is the height, h, of the cone?

a) 10 feet
b) 12 feet
c) 16 feet
d) 20 feet

Answer 1

To find the height (h) of the cone, we can use the Pythagorean theorem. The slant height (L) is the hypotenuse, the radius of the base (r) is one of the legs, and the height (h) is the other leg.

Step-by-step explanation:

To find the height (h) of the cone, we can use the Pythagorean theorem. The slant height (L) is the hypotenuse, the radius of the base (r) is one of the legs, and the height (h) is the other leg. So we have:

L^2 = r^2 + h^2

Given that the slant height (L) is 20 feet and the diameter (d) of the base is 24 feet, we can use the formula for the radius (r) of a circle: r = d/2. Substituting the values:

(20)^2 = (24/2)^2 + h^2

400 = 12^2 + h^2

400 = 144 + h^2

256 = h^2

h = ±16

Therefore, the height (h) of the cone is 16 feet, so the correct answer is c) 16 feet.

Answer 2

The correct answer is C.

3:4:5 = 12:16:20