Question

The surface area of a cone is square units. the height of the cone is times greater than the radius. what is the length of the radius of the cone to the nearest foot? the radius is about feet.

Answer 1

The radius of the cone is 7 feet

How to determine the radius?

The given parameters are:

Surface Area, A = 216π

h = 8/3r

The surface area of a cone is:

$A = \pi r(r + \sqrt{h^2 + r^2})$

So, we have:

$216\pi = \pi r(r + \sqrt{(8/3r)^2 + r^2})$

Factor out r

$216\pi = \pi r(r + r\sqrt{(8/3)^2 + 1})$

Evaluate the exponent

$216\pi = \pi r(r + r * 2.85)$

Evaluate the sum

$216\pi = \pi r(3.85r)$

Divide both sides by pi

$216 = 3.85r^2$

Divide both sides by 3.85

$56.10 = r^2$

Take the square roots of both sides

r = 7 (approximately)

Hence, the radius of the cone is 7 feet

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