Question

The formula for the slant height of a cone is , where S is surface area of the cone. Use the formula to find the slant height, l, of a cone with a surface area of 500π ft2 and a radius of 15 ft. l = ft

Answer 1

we know that

The formula of the surface area of the cone is equal to

$SA=\pi r^{2}+\pi rl$

where

SA is the surface area

r is the radius of the cone

l is the slant height

in this problem we have

$SA=500\pi\ ft^{2}\\r=15\ ft\\l=?$

Solve the formula for l

$SA=\pi r^{2}+\pi rl\\ \\\pi rl=SA-\pi r^{2} \\ \\l=\frac{SA-\pi r^{2} }{\pi r}$

substitute the values

$l=\frac{500\pi -\pi 15^{2} }{\pi15}\\ \\l=\frac{275}{15}\ ft\\ \\l=\frac{55}{3}\ ft\\ \\l=18\frac{1}{3}\ ft$

therefore

the answer is

The slant height is $18\frac{1}{3}\ ft$

Answer 2

Answer:

The formula for the slant height of a cone is , where S is surface area of the cone. Use the formula to find the slant height, l, of a cone with a surface area of 500π ft2 and a radius of 15 ft. l = ft         Answer: 275 ft