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.

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 - 10b - 17 = -3b + 1
b² - 10b - 17 - 1 = -3b
b² - 10b + 3b - 18 = 0
b² - 7b - 18 = 0

Next, factor the quadratic equation:

b² - 7b - 18 = 0
(b + 2)(b - 9) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (b + 2) or (b - 9) must equal zero:

If (b + 2) = 0, b must equal -2
If (b - 9) = 0, b must equal 9

So the solution is that b = -2 or 9

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 40 as well and sum (Inside, Outside) to equal -13. For this problem, those two numbers are -8 and -5. Then, plug these into a set of binomials using the square root of the First variable (y²):

y² - 13y + 40
y² + (-8 - 5)y + (-8 x -5)
(y - 8)(y - 5)

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.

The volume of a cylinder is πr²h:

v = πr²h
v = π(6² x 8)
v = 288π