Question

The formula for the slant height of a cone is t equals StartFraction S minus pi r squared Over pi EndFraction. , 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.

Answer 1

Given:

The formula for the slant height of a cone is t equals StartFraction S minus pi r squared Over pi EndFraction. , where S is the 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.

To find:

The slant height, l, of a cone with a surface area of 500π ft2 and a radius of 15 ft.

Solution:

The given formula for the slant height of the cone is,

$\boxed{\bold{t = S - \pi r^2}}$

where t = slant height of the cone, S = surface area of the cone and r = radius of the cone

Here we have,

Slant height = "l" ft

The surface area of the cone = 500π ft²

The radius of the cone = 15 ft

Now, by substituting the given values in the formula of slant height above, we get

$l = 500\pi - \pi (15)^2$

$\implies l = 500\pi - 225\pi$

$\implies \bold{l = 275\pi\:ft}$

Thus, the slant height, l, of a cone with a surface area of 500π ft² and a radius of 15 ft is → 275π ft².

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