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

Answer 1

To find the surface area of the soap bar, we need to find the surface area of the cylindrical side and the surface area of the top and bottom.

Surface area of the cylindrical side:
The formula for the surface area of a cylinder is 2πrh, where r is the radius and h is the height. Since the diameter is 5 cm, the radius is half of that, which is 2.5 cm. So, the surface area of the cylindrical side is:
2π(2.5)(2) = 10π cm^2

Surface area of the top and bottom:
The formula for the surface area of a circle is πr^2, where r is the radius. So, the surface area of the top and bottom of the cylinder is:
2(π)(2.5)^2 = 2(π)(6.25) = 12.5π cm^2

Therefore, the total surface area of the soap bar is:
10π + 12.5π = 22.5π ≈ 70.69 cm^2

So, the surface area of the soap bar is approximately 70.69 square centimeters.