Question

Students were packed shoulder to shoulder in a gym for a pep rally. The students were in a rectangular shaped area of 7,500

ft. If each student on average took up a circular space with a diameter of 2.5 ft what is the best estimate for the number of
students at the pep rally?
A)600
B)900
C)1,200
D)1,800​

Answer 1

c)1200

Explanation:

Given: Students were packed shoulder to shoulder in a gym for a pep rally. The students were in a rectangular shaped area of
`7500` ft.

To Find: If each student on average took up a circular space with a diameter of
`2.5` ft what is the best estimate for the number of students at the pep rally.

Solution:

Consider the figures attached

A student took up a circular space, if they were packed in rows each student acquired a circular space of
`2.5` ft and left some unused area as given in figures

Now,

Area acquired by a student is a square of side
`2.5` ft as given in figure

Area acquired by single student
`=(\text{length of square})^2`

`=2.5*2.5`

`6.25\text{sq.ft}`

Total number of students
`=\frac{\text{total area of rectangular gym}}{\text{area acquired by single student}}`

`(7500)/(6.25)`

`1200`

there are approximately
`1200` students in gym hence option b is correct.