Answered

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A cone has a surface area of 200 pi square inches. If the radius of the
cone is 10 inches, find the length of the slant height.

Sagot :

Corsaquix

Answer:

[tex]20\:\mathrm{in}[/tex]

Step-by-step explanation:

The lateral surface area of a cone is given by [tex]A=\pi r\ell[/tex], where [tex]r[/tex] is the radius of the base of the cone and [tex]\ell[/tex] is the cone's slant height.

Solving for [tex]\ell[/tex]:

[tex]200\pi=10\pi\ell,\\\ell=\frac{200\pi}{100\pi}=\boxed{20\:\mathrm{in}}[/tex]

*Note: It is implied that the surface area of 200 pi square inches is lateral surface area and not total surface area, because it is impossible to obtain a total surface area of 200 pi with a radius of 10 inches.

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