Question

A forest ranger can see a distance of 42km in all directions. how many square kilometers can she observe?

Answer 1

The area that the forest ranger can observe is approximately 5536 square kilometers, calculated using the area of a circle formula with the visibility range as the radius.

Step-by-step explanation:

Calculating the Area of Observation for a Forest Ranger

The question at hand involves determining the area that a forest ranger can observe given a visibility range. In this scenario, the forest ranger can see up to a distance of 42 km in all directions. This establishes a circular area of visibility with the ranger at the center. The formula for the area of a circle is given by A = πr^2, where A is the area and r is the radius, which in this case is the distance the ranger can see.

Applying the formula, we can calculate the area as follows:

A = π * (42 km)^2

= π * (42 km * 42 km)

= π * 1764 km^2

= 5536 km^2 (approx.)

Therefore, the forest ranger can observe approximately 5536 square kilometers.

Note that when performing such calculations it is important to be aware that the visibility distance can be affected by the height of observation and refraction, which are not taken into account in this simplistic calculation.

Answer 2

5541.76 km²

Step-by-step explanation:

The area a forest ranger can observe is in the shape of a circle, where the radius of the circle represents the distance she can see in all directions.

The formula to calculate the area of a circle is:

`\text{Area} = \pi * \text{radius}^2`

Given that the ranger can see a distance of 42 km in all directions, the radius of the circle is 42 km.

`\text{Area} = \pi * 42^2 \\\\ \text{Area} = \pi * 1764\\\\\sf Approximating \:\pi \: as\: 3.14\\\\\text{Area} \approx 3.14 * 1764 \\\\ \text{Area} \approx 5541.76 \, \text{square kilometers}`

Therefore, the forest ranger can observe approximately 5541.76 square kilometers.