A cosmetics company that makes small cylindrical bars of soap wraps the bars in plastic prior to shipping. Find the surface area of a bar of soap if the diameter is 5 cm and the height is 2 cm. Use 3.14 for π. Round to the nearest tenth. Remember do not round until the very end.
First, we need to find the lateral surface area of the cylinder, which is the surface area without the top and bottom.
Lateral Surface Area = 2 * π * r * h
Lateral Surface Area = 2 * 3.14 * 2.5 * 2
Lateral Surface Area = 31.4 cm²
Next, we need to find the surface area of the top and bottom of the cylinder.
Top and Bottom Surface Area = 2 * π * r²
Top and Bottom Surface Area = 2 * 3.14 * (2.5)²
Top and Bottom Surface Area = 2 * 3.14 * 6.25
Top and Bottom Surface Area = 39.25 cm²
Now, we can find the total surface area by adding the lateral surface area and the top and bottom surface area.
Total Surface Area = Lateral Surface Area + Top and Bottom Surface Area
Total Surface Area = 31.4 + 39.25
Total Surface Area = 70.65 cm²
Therefore, the surface area of a bar of soap with a diameter of 5 cm and a height of 2 cm is 70.65 cm².