Question

modeling real life a farmer fills a field with solar - panels. the area of the field is 32,374.9 square meters.
a. about how many solar panels of the size shown can fit in the field? explain.
165.1 cm
99 cm
b. one solar panel of this size can produce about 1.06 kilowatt - hours of electricity per day. on average, a house uses about 1000 kilowatt - hours of electricity per month. can the field produce enough electricity for 500 houses each month?

Explanation:

Step1: Calculate area of one solar - panel

First, convert the dimensions of the solar - panel from centimeters to meters. $165.1\ cm=1.651\ m$ and $99\ cm = 0.99\ m$. The area of a rectangle is $A = l\times w$. So, the area of one solar - panel $A_{panel}=1.651\times0.99 = 1.63449\ m^{2}$.

Step2: Find number of solar - panels that can fit in the field

Divide the area of the field by the area of one solar - panel. Let $n$ be the number of solar - panels. $n=\frac{32374.9}{1.63449}\approx19807.33$. So, about 19807 solar - panels can fit in the field.

Step3: Calculate total electricity production per day

If one solar - panel produces 1.06 kilowatt - hours per day, and there are about 19807 solar - panels, the total electricity production per day $E_{day}=19807\times1.06 = 20995.42$ kilowatt - hours.

Step4: Calculate total electricity production per month

Assume a month has 30 days. So, the total electricity production per month $E_{month}=20995.42\times30 = 629862.6$ kilowatt - hours.

Step5: Calculate electricity needed for 500 houses per month

If one house uses 1000 kilowatt - hours per month, for 500 houses, the electricity needed per month $E_{houses}=500\times1000 = 500000$ kilowatt - hours.

Step6: Compare the two amounts

Since $629862.6>500000$, the field can produce enough electricity for 500 houses each month.

Answer:

a. About 19807 solar - panels can fit in the field.
b. Yes, the field can produce enough electricity for 500 houses each month.