Question

Suppose the radius of a circle is \color{purple}{3}3start color purple, 3, end color purple. what is its circumference?either enter an exact answer in terms of \piπpi or use 3.143.143, point, 14 for \piπpi and enter your answer as a decimal.

Answer 1

The circumference of a circle with a radius of 3 is 6π when expressed exactly in terms of π, or approximately 18.84 if using 3.14 as an approximation for π.

Step-by-step explanation:

To find the circumference of a circle with a radius of 3, we can use the formula C = 2πr, where π (pi) is a mathematical constant approximately equal to 3.14159, and r is the radius of the circle. As specified, we can use either an exact answer in terms of π or use the approximate value of 3.14 for π.

Using π, the exact circumference is calculated as:

C = 2π(3) = 6π

Using the approximate value of 3.14 for π, we calculate the circumference as:

C = 2 × 3.14 × 3 = 18.84

Therefore, the circumference of the circle can either be expressed exactly as 6π or approximately as 18.84, if using the numerical approximation of π.

Answer 2

`\text{Consider the circle of radius 3.}\\ \\ \text{we need to find the cirumference of the circle.}\\ \\ \text{we know that the circumference of the circle of radius r is given by}\\ \\ \text{circumference}=2\pi r\\ \\ \text{so using this formula, the circumference of the given circle is}`

`\text{Circumference}=2\pi r\\ \\ =2\pi * 3\\ \\ =6\pi \\ \text{so the circumference of the circle is}=6\pi\\ \\ \text{and in decimals, it gives}=6* 3.14\\ \\ \Rightarrow \text{circumference}=18.84`

Hence the circumference of the circle is: 6π or 18.84 units