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.

Answer 1

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.