Question

I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER

Answer 1

`A = 297\pi`

Explanation:

To solve this problem we need to be familiar with the formula for the surface area of a cone:

`A = \pi r(r + √(h^2+r^2))`

We are given the length of a side and the diameter, to calculate the radius divide the diameter in half:

`r = (d)/(2)\\r = (18)/(2)\\r = 9 cm`

To calculate the height of the cone, we must use the Pythagorean Theorem:

`C^2 = A^2 + B^2`

We can treat the side length as the hypotenuse
`C`, the radius as the base
`A`, and solve for height
`B`. Set the expression up like this:

`C^2 = A^2 + B^2\\24^2 = 9^2 + B^2\\B^2 = 24^2 - 9^2\\B = √(24^2 - 9^2)\\B = √(576 - 81)\\B = √(495)\\B \approx 22.25`

Now we can plug into our original formula:

`A = \pi r(r + √(h^2+r^2))\\A = \pi 9(9+\sqrt{√(495)^2+9^2}\\A = \pi 9(9+√(495 + 81)\\A = \pi 9(9+√(576))\\A = \pi 9(9 + 24)\\A = \pi 9(33)\\A = 297\pi`