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

c² = a² + b²
c² = 8² + 5²
c² = 64 + 25
c² = 89
c = \( \sqrt{89} \)

The circumference of a circle is the distance around its perimeter and equals π (approx. 3.14159) x diameter: c = π d. The area of a circle is π x (radius)² : a = π r².

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 = \( \sqrt{a} \) = \( \sqrt{36} \) = 6

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 = 6² + 6²
c² = 72
c = \( \sqrt{72} \) = \( \sqrt{36 x 2} \) = \( \sqrt{36} \) \( \sqrt{2} \)
c = 6\( \sqrt{2} \)

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

sa = 2πr² + 2πrh
sa = 2π(1²) + 2π(1 x 6)
sa = 2π(1) + 2π(6)
sa = (2 x 1)π + (2 x 6)π
sa = 2π + 12π
sa = 14π

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.

4c + 3y = 2c + 2y - 6
4c = 2c + 2y - 6 - 3y
4c - 2c = 2y - 6 - 3y
2c = -y - 6
c = \( \frac{-y - 6}{2} \)
c = \( \frac{-y}{2} \) + \( \frac{-6}{2} \)
c = -\(\frac{1}{2}\)y - 3