To determine the number of square feet of tree wrap required for tree 1, we'll break down the calculation into the following steps:
1. Determine the diameter and circumference of tree 1 in year 13.
- The diameter of tree 1 in year 13 is given as 22.2 inches.
- To find the circumference ([tex]\( C \)[/tex]), we use the formula for the circumference of a circle: [tex]\( C = \pi \times D \)[/tex], where [tex]\( D \)[/tex] is the diameter. Thus,
[tex]\[
C = \pi \times 22.2 \approx 69.7433569096934 \text{ inches}
\][/tex]
2. Calculate the area of the tree wrap in square inches.
- The height of the tree wrap is given as 45 inches.
- To find the area of the wrap ([tex]\( A \)[/tex]), we use the formula for the area of a rectangle: [tex]\( A = C \times H \)[/tex], where [tex]\( H \)[/tex] is the height. Thus,
[tex]\[
A = 69.7433569096934 \times 45 \approx 3138.4510609362032 \text{ square inches}
\][/tex]
3. Convert the area from square inches to square feet.
- There are 144 square inches in 1 square foot.
- So, the area in square feet ([tex]\( A_{\text{ft}} \)[/tex]) is found by dividing the area in square inches by 144:
[tex]\[
A_{\text{ft}} = \frac{3138.4510609362032}{144} \approx 21.79479903427919 \text{ square feet}
\][/tex]
4. Round the area to the nearest whole number.
- Rounding 21.79479903427919 to the nearest whole number gives us 22 square feet.
So, the number of square feet of wrap needed is:
22 square feet.
Therefore, the correct answer is:
A. 22
