Remember the formula for the area of a circle? Πr(squared) (pi*radius squared). We are going to apply that here. The formula for the area of a cylinder is Πr(squared)*h (pi*radius squared*height). Why are we multiplying the height? Think of it like this; each unit of height is one layer of the cylinder. A layer could be, perhaps, a building block, or a story of a building. So if the cylinder is 6 inches high, it has 6 layers, or if it is 10 feet high, it has 10 layers. Each layer is in the shape of a circle. If you find the area of one circle and then multiply it by the number of circles, you get the area of the cylinder, and you get your final answer!
Ok, so the formula is Πr(squared)*h. The cylinder in this example has a radius of 2 inches, a diameter of 4 inches, and a height of 6 inches. Let’s plug in the numbers. Now the formula becomes Π2(squared)*6.
Use order of operations to solve the problem. Π2(squared)*6 becomes
4Π*6. This in turn becomes 24Π inches cubed. You can use this as your final answer, or you can solve this. Your final answer then is 75.36 inches cubed. (Don’t forget units!)
Why is the final answer now cubed, instead of squared? Look at the problem. You have three times where you use multiplication. When you did radius squared, that is two uses for multiplication (radius times radius). Then you multiply THAT by the height, making for a third time.