Question

draw a circle with the given center point that has a circumference of approximately 43.98 units on the grid below. to draw the circle, first identify the center point. then plot a point on the circumference of the circle.

Explanation:

Step1: Recall Circumference Formula

The formula for the circumference of a circle is \( C = 2\pi r \), where \( C \) is the circumference and \( r \) is the radius. We know \( C \approx 43.98 \) units.

Step2: Solve for Radius

Substitute \( C = 43.98 \) into the formula: \( 43.98 = 2 \times \pi \times r \). Using \( \pi \approx 3.14 \), we have \( 43.98 = 2 \times 3.14 \times r \). Simplify the right - hand side: \( 6.28r = 43.98 \). Then, solve for \( r \) by dividing both sides by 6.28: \( r=\frac{43.98}{6.28}=7 \) units.

Step3: Locate Center and Plot Circle

The given center point (let's assume the center is at, for example, (16, 14) from the grid). To draw the circle, we use a compass (or the drawing tool) with a radius of 7 units (since each grid square can be considered as 1 unit). We measure 7 units from the center in all directions (up, down, left, right, and diagonally) to plot points on the circumference. For example, if the center is (16, 14), then a point on the circumference could be (16 + 7, 14)=(23, 14), or (16, 14 + 7)=(16, 21), etc.

Answer:

First, find the radius using \( C = 2\pi r \). With \( C\approx43.98 \) and \( \pi\approx3.14 \), \( r = 7 \). Then, identify the center point (from the grid, e.g., (16, 14)) and draw a circle with radius 7 units. A point on the circumference (using center (16, 14)) could be (23, 14) (or other points 7 units from the center).