Question

Type the correct answer in the box. Use numerals instead of words. 5 The surface area of a cone is 2167 square units. The height of the cone is 3 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 surface area of the cone is the amount of space on it, the radius of the cone is about 13 feet

How to determine the radius?

The given parameters are:

• Surface Area, A = 2167
• Height (h) = 3 * radius (r)

The surface area is calculated using:

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

So, we have:

$A =\pi r(r + \sqrt{(3r)^2 + r^2})$

Substitute 2167 for A

$2167 =\pi r(r + \sqrt{(3r)^2 + r^2})$

Evaluate the sum

$2167 =\pi r(r + \sqrt{10r^2})$

Divide both sides by $\pi$

$689.78 =r(r + \sqrt{10r^2})$

Evaluate the exponent

$689.78 =r(r + 3.16r)$

Evaluate the sum

689.78 =r(4.16r)

Open the bracket

689.78 = 4.16r²

Divide both sides by 4.15

r² =165.8125

Take the square root of both sides

r = 13 (approximated)

Hence, the radius of the cone is about 13 feet

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