Question

Could you please help me out with a question

Answer 1

Question:

Solution:

First, consider the right triangle inside the circle. Notice that the hypotenuse of the triangle is the radius of the circle, so to find the radius of the circle we can apply the Pythagorean theorem to the right triangle:

`r\text{ = }\sqrt[]{40^2+42^2}\text{ = 58}`

so, the radius of the circle is 58. Now, the area of the circle is given by the following formula:

`A=\pi r^2`

thus, replacing the data obtained (the radius), we obtain that:

`A=\pi58^2\text{ = }3364\pi`

then, the area of the circle is:

`A=\text{ }3364\pi`

On the other hand, the circumference of the circle is given by the following formula:

`C\text{ = 2}\pi r`

thus, replacing the data obtained (the radius), we obtain that:

`C\text{ = 2}\pi(58)\text{ = 116}\pi`

then, the circumference of the circle is:

`C\text{ =116}\pi`