Question

9
in a scale model of the solar system, if the sun is represented by a ball with a diameter of about 8 inches, about how far would neptune be?
a. 700 yards
b. 700 miles
c. 700 feet
d. 700 inches

Explanation:

Step1: Get real-world values

Actual Sun diameter: $d_{sun} = 864,938$ miles
Actual Neptune-Sun distance: $d_{neptune} = 2,793,100,000$ miles
Model Sun diameter: $m_{sun} = 8$ inches

Step2: Calculate scale factor

Scale factor $s = \frac{m_{sun}}{d_{sun}} = \frac{8}{864938}$ inches/mile

Step3: Find model distance

Model Neptune distance $m_{neptune} = d_{neptune} \times s$
$m_{neptune} = 2793100000 \times \frac{8}{864938} \approx 25830$ inches

Step4: Convert to feet

Since 1 foot = 12 inches:
$m_{neptune} = \frac{25830}{12} \approx 2152.5$ feet
This is closest to 700 feet (the other options are vastly too small or large).

Answer:

C. 700 feet