Question

Please help.. surface area of cylinder

Answer 1

Remember that the surface area of an object is the area of all of its faces added up.

The area of one circle is:

$\pi(4)^2 = 16\pi$

The area of the rectangle is a little more complex. We are missing the length of one side, which is the circumference of one of the base circles (think about when the diagram above is made into a three-dimensional cylinder). The circumference of the circles is:

$(2 \cdot 4)\pi = 8\pi$

The area of the rectangle is thus:

$8\pi \cdot 9 = 72\pi$

When all of the areas are added together, we find that the total surface area of the shape is:

$72\pi + 16\pi + 16\pi = \boxed{104\pi}$