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

sa = 2πr² + 2πrh
sa = 2π(6²) + 2π(6 x 7)
sa = 2π(36) + 2π(42)
sa = (2 x 36)π + (2 x 42)π
sa = 72π + 84π
sa = 156π

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 = \( \sqrt{a} \) = \( \sqrt{49} \) = 7

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 = 7² + 7²
c² = 98
c = \( \sqrt{98} \) = \( \sqrt{49 x 2} \) = \( \sqrt{49} \) \( \sqrt{2} \)
c = 7\( \sqrt{2} \)

To combine like terms, add or subtract the coefficients (the numbers that come before the variables) of terms that have the same variable raised to the same exponent.

7a⁴ + 4a⁴ = 11a⁴

To multiply monomials, multiply the coefficients (the numbers that come before the variables) of each term, add the exponents of like variables, and multiply the different variables together.

(8a)(6ab) - (7a²)(6b)
(8 x 6)(a x a x b) - (7 x 6)(a² x b)
(48)(a¹⁺¹ x b) - (42)(a²b)
48a²b - 42a²b
6a²b

To factor a quadratic expression, apply the FOIL (First, Outside, Inside, Last) method in reverse.