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.

Answer 1

To find the surface area of the cylindrical bar of soap, we first need to find the lateral area (the surface area of the side of the cylinder) and the two circular bases.

Lateral area = 2πrh
Lateral area = 2 x 3.14 x 5 cm x 2 cm
Lateral area = 62.8 cm²

Now, let's find the surface area of the two circular bases:
Base area = πr²
Base area = 3.14 x (2.5 cm)²
Base area = 19.625 cm² (for both bases)

Now, let's find the total surface area by adding the lateral area and the two base areas:
Total surface area = Lateral area + 2(Base area)
Total surface area = 62.8 cm² + 2(19.625 cm²)
Total surface area = 62.8 cm² + 39.25 cm²
Total surface area = 102.05 cm²

Therefore, the surface area of a bar of soap with a diameter of 5 cm and a height of 2 cm is 102.05 cm².