To determine the visible area of the bare paper, we find the total area covered by the stickers and subtract it from the total area of the paper. The radius of each sticker is 2 cm, and the paper dimensions are 24 cm by 33 cm. By calculating the areas and subtracting, we find that approximately 188.81 square cm of the bare paper will be visible around the stickers.
Step-by-step explanation:
To determine how much of the bare paper will be visible around the stickers, we first need to calculate the total area covered by the stickers. The area of each sticker can be found using the formula A = πr², where r is the radius. In this case, the radius is 2 cm, so the area of each sticker is A = π(2 cm)² = 4π cm².
Next, we need to find the total number of stickers that can fit in the given dimensions of the paper. The paper is 24 cm by 33 cm, so the area of the paper is 24 cm × 33 cm = 792 cm². Dividing the paper area by the area of each sticker, we get 792 cm² ÷ 4π cm² ≈ 63.62. Since we can't have a fraction of a sticker, we can fit a maximum of 63 stickers on the paper.
To find the visible area of the paper, we subtract the total area covered by the stickers from the total area of the paper. The total area covered by the stickers is 63 stickers × 4π cm² = 252π cm². The total area of the paper is 792 cm². Therefore, the visible area of the bare paper will be 792 cm² - 252π cm² ≈ 188.81 cm². So, the correct option is 188.81 square cm.