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:
[tex]A =\pi r(r + \sqrt{h^2 + r^2})[/tex]
So, we have:
[tex]A =\pi r(r + \sqrt{(3r)^2 + r^2})[/tex]
Substitute 2167 for A
[tex]2167 =\pi r(r + \sqrt{(3r)^2 + r^2})[/tex]
Evaluate the sum
[tex]2167 =\pi r(r + \sqrt{10r^2})[/tex]
Divide both sides by [tex]\pi[/tex]
[tex]689.78 =r(r + \sqrt{10r^2})[/tex]
Evaluate the exponent
[tex]689.78 =r(r + 3.16r)[/tex]
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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