Question

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

Answer 1

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

`D=2r=2*4=8cm`