A cylinder is a solid figure with straight parallel sides and a circular or oval cross section with a radius (r) and a height (h). The volume of a cylinder is π r²h and the surface area is 2(π r²) + 2π rh.

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 first step to solve a quadratic expression that's not set to zero is to solve the equation so that it is set to zero:

b² + 7b - 26 = 4b + 2
b² + 7b - 26 - 2 = 4b
b² + 7b - 4b - 28 = 0
b² + 3b - 28 = 0

Next, factor the quadratic equation:

b² + 3b - 28 = 0
(b - 4)(b + 7) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (b - 4) or (b + 7) must equal zero:

If (b - 4) = 0, b must equal 4
If (b + 7) = 0, b must equal -7

So the solution is that b = 4 or -7

A trapezoid is a quadrilateral with one set of parallel sides.

The first step to solve a quadratic equation that's set to zero is to factor the quadratic equation:

c² - 49 = 0
(c - 7)(c + 7) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (c - 7) or (c + 7) must equal zero:

If (c - 7) = 0, c must equal 7
If (c + 7) = 0, c must equal -7

So the solution is that c = 7 or -7