Look at the cone below.

Question

15 ft15\ \text{ft}15 ft

lll

8 ft8\ \text{ft}8 ft

How many feet long is the slant height of the cone? Click Here for Help Video.

Answer 1

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

Given:

• Height (h) of the cone = 8 ft
• Radius (r) of the base = 15 ft

The formula to find the slant height is:

$$l=\sqrt{r^2+h^2}$$

Substituting the values:

$$l=\sqrt{{15}^2+8^2}$$ $$l=\sqrt{225+64}$$ $$l=\sqrt{289}$$ $$l=17\text{ ft}$$

Therefore, the slant height of the cone is 17 feet.