Question

A game shop sells marbles in clear plastic cylinders. Four marbles fit across the diameter of the cylinder and 10 marbles fit from the base to the top of the cylinder. Each marble has a diameter of 2 cm. What is the area of the plastic that is needed to make one cylinder?

Answer 1

To start, you know that this question is asking for the surface area of one of the cylinders, and the formula to finding the surface area of a cylinder is A=2πrh+2πr^2.

Now, to find the surface area, you first need to figure out the height of the plastic cylinder and its radius. 
Since you know that the diameter (twice the radius) of the cylinder is equivalent to 4 marbles, and each marble has a diameter of 2 cm, the diameter of the cylinder would be 8 cm. Then, to find its radius, you divide by 2, so its radius is 4.
Now, since you know that the height of the cylinder is 10 marbles, you multiply 10 by 2 to get that the height is 20 cm tall. 
Since you now have the values of the height and the radius, plug the values into the surface area of a cylinder formula (r is radius and h is height).
A=2π(4)(20)+2π(4)^2.
Assuming that pi is 3.14, when you simplify this using PEMDAS, you get 
502.4+100.48 which then simplifies to 602.88, the area of the plastic to make one cylinder.