A circle has a centre at (3,5). The point (3,8) is on the circle. What is the circumference of the circle to the nearest tenth?
well, the distance from (3,5) to (3,8) is 3, so that is the radius of the circle.
Now, I'm sure you know the formula for the circumference of a circle, given the radius...
To find the circumference of a circle, we need to use the formula:
Circumference = 2 * π * Radius
Given that the center of the circle is at (3,5) and the point (3,8) is on the circle, we can determine the radius by calculating the distance between the center and the point using the distance formula.
The distance formula is defined as:
Distance = √((x2 - x1)² + (y2 - y1)²)
Applying this formula to our case, where (x1, y1) = (3, 5) (the center) and (x2, y2) = (3, 8) (the point on the circle), we have:
Distance = √((3 - 3)² + (8 - 5)²)
= √(0² + 3²)
= √(0 + 9)
= √9
= 3
Now that we have the radius, we can plug it into the circumference formula, using an approximation of π as 3.14:
Circumference = 2 * 3.14 * Radius
= 2 * 3.14 * 3
= 18.84
Therefore, the circumference of the circle is approximately 18.84 to the nearest tenth.