Answer:
192π [tex]in^{2}[/tex]
Step-by-step explanation:
A cylinder is made up of 2 circles and a rectangle. To get the surface area you need add the area of the two circles with the area of the rectangle.
The equation for the area of a circle is π[tex]r^{2}[/tex] where r is the radius. Because we are getting surface area, we need the circle on top of the cylinder and the circle on the bottom of the cylinder. We can re-write the surface area of both circles as 2π[tex]r^{2}[/tex]
You also need to find the circumference of a circle (which will end up being the width of the rectangle) and the height (10 inches)
The circumference of the circle is 2πr and because its essentially a rectangle that has been curved around a circle, we can multiply its height by length to get 20 [tex]in^{2}[/tex]πr area
Putting all the parts together we get:
Surface Area of cylinder = 2π[tex]r^{2}[/tex] + 20πr
using the 6 inches given in the problem to find the exact surface area we get:
(36 [tex]in^{2}[/tex])(2)π + (20 [tex]in^{2}[/tex])(6 in) = (120 + 72)π[tex]in^{2}[/tex] = 192π[tex]in^{2}[/tex]
