The circumference of a circle is #11pi# inches. What is the area, in square inches, of the circle?

Question

James Atkins · Accepted Answer

#~~95 "sq in"# We can derive the diameter of the circle by: #"Circumference"=pi*"Diameter"# #"Diameter"="Circumference"/pi=(11pi)/pi=11 "inches"# Hence, the area of the circle: #"Area of circle"=pi*("Diameter"/2)^2=pi*(11/2)^2~~95 "sq in"#

Autumn Armstrong · Answer

The circumference of a circle having radius #r# is #2pir.#

Hence, by what is given, #2pir=11pi rArr r=11/2.#

#":. The Area of the circle="pir^2=pi(11/2)^2=30.25pi" sq. in."#

Noah Atkinson · Answer

#color(red)(95# inches² to nearest inch²

circumference of a circle#=2pir# circumference given#=11pi# #:.2pir=11pi# divide L.HS.and R.H.S. by # pi # #:.2r=11# #:.r=11/2# #:.r=5.5# Area of the circle #=pir^2=pi*(5.5)^2# #:.=3.141592654*(5.5)^2# #:.color(red)(=95# inches². to the nearest inch²

James Atkins · Answer

undefined To find the area of the circle, we'll first need to find its radius. The formula to calculate the circumference of a circle is:

$$ \text{Circumference} = 2\pi r $$

Given that the circumference of the circle is $11\pi$ inches, we can set up the equation:

$$ 11\pi = 2\pi r $$

Solving for $r$:

$$ r = \frac{11\pi}{2\pi} = \frac{11}{2} $$

Now that we have the radius ($r = \frac{11}{2}$), we can use the formula to calculate the area of the circle:

$$ \text{Area} = \pi r^2 $$

Substituting the value of $r$:

$$ \text{Area} = \pi \left(\frac{11}{2}\right)^2 $$

$$ \text{Area} = \pi \times \frac{121}{4} $$

$$ \text{Area} = \frac{121\pi}{4} $$

Therefore, the area of the circle is $ \frac{121\pi}{4} $ square inches.