Raphael K. answered • 09/21/21
I have mastered Algebra 2 and teach it daily.
How would I find the surface area of a cone as a polynomial in standard form?
Here is everything included in the problem.
Write the surface area of the figure as a polynomial in standard form.
S = πr2 + πrℓ
r = 3x
h = 4x+1
Construct a right triangle to represent a slice of the cone, in which the base is the radius 3x and the height is 4x + 1.
Use the pythagorean theorem to get ℓ the slant height, or the hypotenuse of the right triangle.
r2 + h2 = ℓ2
(3x)2 + (4x + 1)2 = ℓ2
9x2 + (4x + 1)(4x + 1) = ℓ2
9x2 + 16x2 + 8x + 1 = ℓ2
√(25x2 + 8x + 1) = √ℓ2
ℓ = √(25x2 + 8x + 1)
With the radius height and slant height as functions of x. Plug them into the following expression:
S = πr + πrℓ
S(x) = π(3x)2 + π(3x)[√(25x2 + 8x + 1)]
Bradford T.
I came up with the same answer, but the problem was wanting it in standard form. For example, coefficients with descending integer degrees of x. Not sure how to do that.09/21/21