The surface area of a cylinder is 2πr² + 2πrh:

sa = 2πr² + 2πrh
sa = 2π(2²) + 2π(2 x 8)
sa = 2π(4) + 2π(16)
sa = (2 x 4)π + (2 x 16)π
sa = 8π + 32π
sa = 40π

To find the diagonal we need to know the length of one of the square's sides. We know the area and the area of a square is the length of one side squared:

a = s²

so the length of one side of the square is:

s = \( \sqrt{a} \) = \( \sqrt{16} \) = 4

The Pythagorean theorem defines the square of the hypotenuse (diagonal) of a triangle with a right angle as the sum of the squares of the other two sides:

c² = a² + b²
c² = 4² + 4²
c² = 32
c = \( \sqrt{32} \) = \( \sqrt{16 x 2} \) = \( \sqrt{16} \) \( \sqrt{2} \)
c = 4\( \sqrt{2} \)

A monomial contains one term, a binomial contains two terms, and a polynomial contains more than two terms.

To solve this equation, isolate the variable for which you are solving (c) on one side of the equation and put everything else on the other side.

-5c - 5y = 2c - 7y - 8
-5c = 2c - 7y - 8 + 5y
-5c - 2c = -7y - 8 + 5y
-7c = -2y - 8
c = \( \frac{-2y - 8}{-7} \)
c = \( \frac{-2y}{-7} \) + \( \frac{-8}{-7} \)
c = \(\frac{2}{7}\)y + 1\(\frac{1}{7}\)

According to the Pythagorean theorem, the hypotenuse squared is equal to the sum of the two perpendicular sides squared:

c² = a² + b²
c² = 2² + 3²
c² = 4 + 9
c² = 13
c = \( \sqrt{13} \)