Question

guided practice a hot air balloon needs to land in this field. what is the geometric probability that the balloon will land in the pond instead of the field? round your answer to the nearest tenth. a. 86.9% b. 20.8% c. 6.5% d. 93.4% chart: a rectangle labeled field with length 200 ft and width 150 ft, and a circle labeled pond with radius 25 ft at the bottom - left corner of the rectangle

Explanation:

Step1: Calculate field area

$A_{\text{field}} = 200 \times 150 = 30000 \, \text{ft}^2$

Step2: Calculate pond area

$A_{\text{pond}} = \pi r^2 = \pi (25)^2 = 625\pi \approx 1963.5 \, \text{ft}^2$

Step3: Compute geometric probability

$P = \frac{A_{\text{pond}}}{A_{\text{field}}} \times 100\% = \frac{1963.5}{30000} \times 100\% \approx 6.5\%$

Answer:

C. 6.5%