A right cylinder has a radius of (2x+3) inches and a height of (6x+1) inches. Which polynomial equals the surface area of the cylinder? Use the formula S.A=2pirh + 2pir^2 for the surface area of the cylinder.
The surface area of the cylinder can be found using the formula S.A = 2πrh + 2πr^2. Substituting the given values for the radius and height:
S.A = 2π(2x + 3)(6x + 1) + 2π(2x + 3)^2
Expanding and simplifying:
S.A = 2π(12x^2 + 2x + 18x + 3) + 2π(4x^2 + 12x + 9)
S.A = 2π(12x^2 + 20x + 3) + 2π(4x^2 + 12x + 9)
S.A = 24πx^2 + 40πx + 6π + 8πx^2 + 24πx + 18π
Combining like terms:
S.A = 32πx^2 + 64πx + 24π
Therefore, the polynomial that equals the surface area of the cylinder is 32πx^2 + 64πx + 24π.