Question

Using the formula A/π=r, find the length of the radius if the area is 25 square centimeters. Show your work, rounding the final answer to the nearest tenth of a centimeter.

Answer 1

To find the radius of a circle with an area of 25 square centimeters, divide the area by π and then take the square root of that result. The radius is approximately 2.8 cm when rounded to the nearest tenth.

Step-by-step explanation:

To find the radius when the area of a circle is given and is 25 square centimeters, we can use the formula A = πr², which can be rearranged to solve for the radius, r, as r = √(A/π). Plugging in the value for A:

First, divide the area by π: 25 cm² / 3.14... = 7.9577 cm² (rounded to eight-digit output as in the calculator example).

Next, take the square root of 7.9577 cm² to find the radius: r ≈ √(7.9577 cm²) = 2.82 cm.

Therefore, the radius of the circle is approximately 2.8 cm when rounded to the nearest tenth of a centimeter.

Answer 2

The length of the radius, using the formula A/π = r with an area of 25 square centimeters, is approximately r ≈ 2.82 centimeters.

Explanation:

To find the length of the radius, we use the formula A/π = r, where A is the area and π is the mathematical constant approximately equal to 3.14159. Given the area A = 25 square centimeters, we substitute this into the formula:

r = 25/π

Using the value of π, we get:

r ≈ 25/3.14159 ≈ 7.9577

Rounding to the nearest tenth of a centimeter, the length of the radius is approximately r ≈ 7.96 centimeters.

This calculation demonstrates how to use the formula A/π = r to find the length of the radius when the area is given. It involves a straightforward substitution and arithmetic to obtain the numerical value of the radius, rounding it to the specified precision.