The diameter of a cone is 14 inches and the height of the cone is 22 inches. Find the slant height of the cone to the nearest tenth of an inch.

1 answer

To find the slant height of the cone, we can use the Pythagorean theorem. The slant height (l) of the cone, the radius (r) of the base, and the height (h) form a right triangle.

Given:
Diameter (d) = 14 inches
Radius (r) = d/2 = 14/2 = 7 inches
Height (h) = 22 inches

Using the Pythagorean theorem:
l^2 = r^2 + h^2
l^2 = 7^2 + 22^2
l^2 = 49 + 484
l^2 = 533
l = sqrt(533)
l ≈ 23.1 inches

Therefore, the slant height of the cone is approximately 23.1 inches.