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 500Ο€ ft2 and a radius of 15 ft. l = ft

Accepted Solution

we know thatThe formula of the surface area of the cone is equal to[tex]SA=\pi r^{2}+\pi rl[/tex]whereSA is the surface arear is the radius of the conel is the slant height in this problem we have[tex]SA=500\pi\ ft^{2}\\r=15\ ft\\l=?[/tex]Solve the formula for l[tex]SA=\pi r^{2}+\pi rl\\ \\\pi rl=SA-\pi r^{2} \\ \\l=\frac{SA-\pi r^{2} }{\pi r}[/tex]substitute the values[tex]l=\frac{500\pi -\pi 15^{2} }{\pi15}\\ \\l=\frac{275}{15}\ ft\\ \\l=\frac{55}{3}\ ft\\ \\l=18\frac{1}{3}\ ft[/tex]thereforethe answer isThe slant height is [tex]18\frac{1}{3}\ ft[/tex]