Question

A circle has a circumference of 10 inches. Find its approximate radius, diameter and area

Answer 1

Radius = 1.59 in

Diameter = 3.18 in

Area = 7.94 in²

Step-by-step explanation:

The circumference of a circle can be calculated as:

`C=2\pi r`

Where r is the radius of the circle and π is approximately 3.14. So, replacing C by 10 in and solving for r, we get:

`\begin{gathered} 10\text{ in = 2}\pi r \\ \frac{10\text{ in}}{2\pi}=(2\pi r)/(2\pi) \\ 1.59\text{ in = r} \end{gathered}`

Then, the radius is 1.59 in.

Now, the diameter is twice the radius, so the diameter is equal to:

Diameter = 2 x r = 2 x 1.59 in = 3.18 in

On the other hand, the area can be calculated as:

`A=\pi\cdot r^2`

So, replacing r = 1.59 in, we get:

`\begin{gathered} A=3.14*(1.59)^2 \\ A=3.14*2.53 \\ A=7.94in^2 \end{gathered}`

Therefore, the answer are:

Radius = 1.59 in

Diameter = 3.18 in

Area = 7.94 in²