Question

PLEASE BE QUICK! WILL GIVE 100 POINTS! THANK YOUUU! <3

A makeup artist purchased some lipsticks and wants to wrap them individually with gift wrap. Each lipstick has a radius of 0.4 inch and a height of 2.2 inches. How many total square inches of gift wrap will the makeup artist need to wrap 5 lipsticks? Leave the answer in terms of π.

10.4π square inches
4.8π square inches
2.08π square inches
1.76π square inches

Answer 1

10.4
`\pi` square inches for all 5 lipsticks

Explanation:

Let's start with by calculating the wrapping needed for the TUBE area of the lipstick. If you've ever unwrapped a tube (like the wrapper on a bottle of soda), it's a rectangle.

The circumference of the lipstick will be the width of the wrap needed for the TUBE part:

Circumference = 2
`\pi r`

= 2 * .4 *
`\pi`

= 0.8
`\pi`

So now multiply that x 2.2

= 0.8
`\pi` * 2.2

= 1.76
`\pi` square inches for 1 lipstick

Now multiply that x 5!

1.76
`\pi` * 5 = 8.8
`\pi` square inches for just the tube part for all 5 lipsticks.

Now the top & bottom (circles) of the lipstick, to calc that area =
`\pi r^(2)` =
`\pi .4^(2)` = 0.16
`\pi` for one circle. There are 2 circles (top & bottom) so 0.16 x 2 = 0.32
`\pi`.

For all 5, 0.32
`\pi` * 5 = 1.6
`\pi`square inches for the top & bottom of all 5 lipsticks.

Now add them up:

8.8 + 1.6 = 10.4
`\pi` square inches for all 5 lipsticks