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

2 Answers
Jan 12, 2018

#"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"#

Jan 12, 2018

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