Answer:
[tex]A = 297\pi[/tex]
Step-by-step explanation:
To solve this problem we need to be familiar with the formula for the surface area of a cone:
[tex]A = \pi r(r + \sqrt{h^2+r^2})[/tex]
We are given the length of a side and the diameter, to calculate the radius divide the diameter in half:
[tex]r = \frac{d}{2}\\r = \frac{18}{2}\\r = 9 cm[/tex]
To calculate the height of the cone, we must use the Pythagorean Theorem:
[tex]C^2 = A^2 + B^2[/tex]
We can treat the side length as the hypotenuse [tex]C[/tex], the radius as the base [tex]A[/tex], and solve for height [tex]B[/tex]. Set the expression up like this:
[tex]C^2 = A^2 + B^2\\24^2 = 9^2 + B^2\\B^2 = 24^2 - 9^2\\B = \sqrt{24^2 - 9^2}\\B = \sqrt{576 - 81}\\B = \sqrt{495}\\B \approx 22.25[/tex]
Now we can plug into our original formula:
[tex]A = \pi r(r + \sqrt{h^2+r^2})\\A = \pi 9(9+\sqrt{\sqrt{495}^2+9^2}\\A = \pi 9(9+\sqrt{495 + 81}\\A = \pi 9(9+\sqrt{576})\\A = \pi 9(9 + 24)\\A = \pi 9(33)\\A = 297\pi[/tex]
