Respuesta :
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circle area=pi.r^2
rectangle area=length. width
22/7.r^2=2.11
r^2=22.7/22
r^2=7
r=square root of 7
circle area=pi.r^2
rectangle area=length. width
22/7.r^2=2.11
r^2=22.7/22
r^2=7
r=square root of 7
Answer:
The radius of the circle is, [tex]\sqrt{7}[/tex] ft
Step-by-step explanation:
Area of the circle(A) and Area of rectangle(A') is given by
[tex]A = \pi r^2[/tex] .....[1]
where, r is the radius of the circle
and
A' = lw ....[2]
where, l is the length and w is the width of the rectangle.
As per the statement:
Area of circle equals the area of a rectangle.
⇒A = A'
It is also given that: a measure of rectangle is 2 ft. by 11 ft.
⇒l = 2ft and w = 11 ft
Substitute in [2] we have;
[tex]A' = 2 \times 11 = 22 ft^2[/tex]
Since, A = A'
⇒[tex]\pi r^2 = 22[/tex]
Use [tex]\pi = \frac{22}{7}[/tex]
then;
[tex]\frac{22}{7} r^2 = 22[/tex]
Divide both sides by 22 we have;'
[tex]\frac{1}{7} r^2 = 1[/tex]
Multiply both sides by 7 we have;
[tex]r^2 = 7[/tex]
or
[tex]r = \sqrt{7}[/tex] ft
Therefore, the radius of the circle is, [tex]\sqrt{7}[/tex] ft
