Surface area of a cylinder

Question

What is the surface area of a cylinder with radius of x+2 and height of x+5?

Answer 1

According to the question, the radius of the cylinder = x+2 and its height is x+5

There are 4 steps required to find the surface area.

1. find the circumference of the circular base with radius x+2: P = 2*pi*r = 2*pi*(x+2) = 2pix + 4pi
2. find the area of the circular base with radius x+2: A = pi*r² = pi*(x+2)² = pi(x² +4x +4)
3. find the area of the vertical component of the cylinder with height h = x+5: H = P*(x+5) = (2xpi + 4pi)*(x+5) = 2x²pi + 14xpi + 20pi
4. If the cylinder is open at the top then the surface area is A + H = 3x²pi + 18xpi + 24pi.
5. If the cylinder is a solid, i.e. closed at top and bottom, then the surface area is 2A + H = 4x²pi + 22xpi + 28pi.