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A 104° sector of a circle has an area of 56 square centimeters. Tothe nearest centimeter, what is the diameter of the circle?

Sagot :

Answer:

The diameter is 8cm

Explanation:

Given the following:

[tex]\begin{gathered} \theta=104^o \\ \\ \text{Area(}A)=\pi r^2=56cm^2 \\ \text{Diameter(D)}=2r=\text{?} \end{gathered}[/tex]

From the area of the circle, we can have the value for the radius, r as follows:

[tex]\begin{gathered} \pi r^2=56 \\ r^2=\frac{56}{\pi} \\ \\ r=\sqrt[]{\frac{56}{\pi}}\approx4cm \end{gathered}[/tex]

We can now obtain the diameter by multiplying the radius by 2

[tex]D=2r=2\times4=8cm[/tex]

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