Question

A trampoline has an area of `49pi` square feet. What is the diameter of the trampoline?

Answer 1

`"diameter "=14" feet"`

Explanation:

`"the area of a circle "=pir^2larrcolor(blue)"r is the radius"`

`rArrpir^2=49pi`

`rArrr^2=(49 cancel(pi))/cancel(pi)=49rArrr=sqrt49=7`

`rArr"diameter "=2xx"radius "=2xx7=14" feet"`

Answer 2

Diameter of the trampoline = `14 " feet"`

Explanation:

For this problem we can assume that a trampoline is a circle, so we can hence use the area of a circle formula:

`A = pir^2`

`r - radius`

The area of circle is `49pi`

`=> A = 49pi`

`=> 49 pi = pi r^2`

Now we find the radius....

Divide by pi:

`=> (49 cancel(pi) ) / cancel(pi) = (cancel(pi) r^2)/cancel(pi)`

`=> 49 = r^2`

Taking the square root of each side:

`=> r= pm7 => 7` As cant have negaitve lengths...

We know the diameter is twice the radius...

`D = 2r`

`=> 2 * 7 = color(red) ( 14 " feet" )`

As we are dealing in feet