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

Question

asked Feb 28, 2023 82.7k views

1 Answer

Silas Reinagel · Answer 1 · 2023-03-05T12:20:55+0000

Answer:

The diameter is 8cm

Step-by-step explanation:

Given the following:

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

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

$\begin{gathered} \pi r^2=56 \\ r^2=(56)/(\pi) \\ \\ r=\sqrt[]{(56)/(\pi)}\approx4cm \end{gathered}$

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