Question

A football field is $120$$\mathrm{yards}$ by $53.333$ $\mathrm{yards}$. What is the area of the football field in acres if $1\mathrm{acre}=43560\mathrm{ft}$? Use correct significant figures when answering this question.

Answer 1

Step-1: Find the area of the field in $yards$:

Given : Length of the football field, $\mathrm{l}=120$ $\mathrm{yards}$

Width of the football field, $\mathrm{w}=53.333$ $\mathrm{yards}$

Now area of the football field $=\mathrm{l}\times \mathrm{w}$

$=120\times 53.333$

$=6399.96$ ${\mathrm{yards}}^2$

Step-2: Convert the area of the field into $\mathrm{feet}$:

Since $1\mathrm{yard}=3\mathrm{ft}$

So, $1{\mathrm{yard}}^2=3\times 3{\mathrm{ft}}^2$

Now $6399.96{\mathrm{yards}}^2=6399.96\times 9$

$=57599.64{\mathrm{ft}}^2$

Step-3: Convert the area of the field into $\mathrm{acres}$:

Since, $1\mathrm{acre}=43560\mathrm{ft}$

So, $1\mathrm{ft}=\frac{1}{43560}\mathrm{acre}$

$1{\mathrm{ft}}^2=\frac{1}{43560\times 43560}{\mathrm{acre}}^2$

Now $57599.64{\mathrm{ft}}^2=\frac{57599.64}{43560\times 43560}$

$=0.000030356$

$=3.0356\times {10}^{-5}\mathrm{acre}{s}^2$

Hence, the area of the football field in acres is $3.0356\times {10}^{-5}\mathrm{acre}{s}^2$.