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viva [34]
3 years ago
5

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
Mathematics
2 answers:
liq [111]3 years ago
7 0

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

<u>the answer is</u>

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

alexira [117]3 years ago
3 0

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         <u>Answer: 275 ft</u>

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