Question

A 219-megawatt solar power plant requires approximately 693,500 square meters of land to collect the required amount of energy from sunlight.

(a) If this land area is circular, approximate its radius.
(b) If this land is a sector of a circle with 0= 75°, approximate its radius.

Answer 1

a. The approximate radius of the circular land area is 468.7 meters.

b. The approximate radius of the circular land area is 936.3 meters.

(a) To approximate the radius of the circular land area, we can use the given information that the land area is approximately 693,500 square meters. The formula for the area of a circle is
`(A = \pi r^2)`, where A is the area and (r) is the radius. Solving for (r), we get
`(r = \sqrt{(A)/(\pi)})`. Substituting the given area, we get
`(r \approx \sqrt{(693500)/(\pi)} \approx 468.7)` meters.

(b) If the land is a sector of a circle with a central angle of 75°, we can use the formula for the area of a sector of a circle, which is
`(A = (\theta)/(360) \pi r^2)`, where (A) is the area, (\theta) is the central angle in degrees, and (r) is the radius. Solving for (r), we get
`(r = \sqrt{(A * 360)/(\pi * \theta)})`. Substituting the given area and central angle, we get
`(r \approx \sqrt{(693500 * 360)/(\pi * 75)} \approx 936.3)`meters.