Question

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 5cm and the height is 2cm.

Answer 1

Equation:
`SA=2 \pi r^2+ \pi dh`
diameter is twice the radius.
2.5^2=6.25
6.25 π ≈19.625
5 π ≈15.70
15.70*2=31.4
31.4+19.625=51.025cm^2

Answer 2

Thus, total surface area of soap is
`70.65~cm^2`

Explanation:

We are given the following information in the question:

A cosmetics company that makes small cylindrical bars of soap wraps the bars in plastic prior to shipping.

Diameter of soap = 5 cm

Height of soap = 2 cm

Radius of soap =
`\displaystyle\frac{\text{Diameter}}{2} = (5)/(2) = 2.5~ cm`

Total surface area of soap = Total surface area of cylinder =

`2\pi r h + \pi r^2 = 2\pi r(r+h)`

where h is the height of cylinder and r is the radius of cylinder.

Putting the values, we get,

Total surface area of soap =
`2* 3.14* 2.5(2.5 + 2) = 70.65~cm^2`

Thus, total surface area of soap is
`70.65~cm^2`