Question

Jessica has some round stickers. Each sticker has a radius of 2 cm. She is trying to cover as much of a sheet of paper that is 24 cm by 33 cm as possible without any overlap and modification of the stickers. How much of the bare paper will be visible around the stickers?

Answer 1

Answer:

189.12 cm²

Step-by-step explanation:

If the radius of the stickers is 2 cm, then the diameter of each sticker is 4 cm.

1. Using this, divide each length of the sheet of paper by the diameter of 4 cm to see how many stickers can fit without overlapping.

24 ÷ 4 = 6 stickers

33 ÷ 4 = 8.25 = 8 stickers (only eight whole stickers will fit without overlap)

This means there can be a total of 48 stickers because 6*8 = 48.

2. Find the area of one sticker. The formula for the area of a circle if πr² (pi times radius squared) with 3.14 equal to π.

3.14 · 2² → 3.14 · 4 = 12.56 cm²

3. Multiply the area by the number of stickers that can fit on the sheet of paper (48 stickers).

12.56 · 48 = 602.88 cm²

4. Find the area of the sheet of paper. The formula for the area of a rectangle is length · width.

24 · 33 = 792 cm²

5. Subtract the area of the stickers from the area of the sheet of paper to solve for the remaining bare paper around the stickers.

792 - 602.88 = 189.12 cm²