Question

students want to hold a concert for a new trending band called density celebration. they plan to use the schools soccer field for the event. in order to meet fire code, there can only be one person per three square feet of field. the soccer field measures 150 ft by 300 ft. answer the questions below. 6a. the students remembered from their geometry course that this would require finding density. lets help them out by writing out the formula for density. (worth 1 point) 6b. how would they determine the amount of space that the field covers to use in this formula? (worth 2 points) 6c. how many attendees could be present at the concert? (worth 2 points)

Explanation:

Step1: Recall density formula

Density $
ho=\frac{n}{V}$, where $n$ is the number of entities (in this case, number of people) and $V$ is the volume or area (in this case, area of the field). For area - based density, if we consider $A$ as the area, the formula is $
ho=\frac{n}{A}$.

Step2: Determine field - area

The soccer field is a rectangle. The area formula for a rectangle is $A = l\times w$, where $l = 300$ ft and $w = 150$ ft. So $A=300\times150 = 45000$ square - feet.

Step3: Calculate number of attendees

We know that there can be 1 person per 3 square feet. Let $n$ be the number of attendees. Using the density formula $
ho=\frac{n}{A}$, and since $
ho=\frac{1}{3}$ people per square - foot and $A = 45000$ square feet. We can solve for $n$: $n=
ho\times A$. Substituting the values, $n=\frac{1}{3}\times45000 = 15000$.

Answer:

6A. $
ho=\frac{n}{A}$ (where $
ho$ is density, $n$ is the number of people, and $A$ is the area of the field)
6B. Use the formula for the area of a rectangle $A = l\times w$, with $l = 300$ ft and $w = 150$ ft. The area $A=300\times150 = 45000$ square feet.
6C. 15000