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

sa = 2πr² + 2πrh
sa = 2π(4²) + 2π(4 x 2)
sa = 2π(16) + 2π(8)
sa = (2 x 16)π + (2 x 8)π
sa = 32π + 16π
sa = 48π

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

a² - 10a + 21 = 0
(a - 3)(a - 7) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (a - 3) or (a - 7) must equal zero:

If (a - 3) = 0, a must equal 3
If (a - 7) = 0, a must equal 7

So the solution is that a = 3 or 7

To factor a quadratic expression, apply the FOIL method (First, Outside, Inside, Last) in reverse. First, find the two Last terms that will multiply to produce 7 as well and sum (Inside, Outside) to equal 8. For this problem, those two numbers are 1 and 7. Then, plug these into a set of binomials using the square root of the First variable (y²):

y² + 8y + 7
y² + (1 + 7)y + (1 x 7)
(y + 1)(y + 7)

The volume of a cylinder is πr²h:

v = πr²h
v = π(5² x 7)
v = 175π

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.

(6a)(3ab) - (4a²)(9b)
(6 x 3)(a x a x b) - (4 x 9)(a² x b)
(18)(a¹⁺¹ x b) - (36)(a²b)
18a²b - 36a²b
-18a²b