Answer :
The assertion is correct. If the circumference of a circle is 176 cm, then its radius is indeed 28 cm.
The reason behind this is the formula for the circumference (c) of a circle:
c = 2πr
where:
- c is the circumference (distance around the circle)
- π (pi) is a mathematical constant approximately equal to 3.14159
- r is the radius (distance from the center of the circle to any point on the circle's edge)
In this case, we are given the circumference (c) as 176 cm. We want to find the radius (r).
Here's how we can use the formula to solve for the radius:
1. Rewrite the formula to isolate r:
Since we want to find r, we can rearrange the formula to have r by itself:
r = c / (2π)
2. Plug in the given value of c and solve for r:
We are given c = 176 cm and π ≈ 3.14159. Substitute these values into the formula:
r = 176 cm / (2 * 3.14159) ≈ 28.01 cm
Since the radius is a measurement of length, we typically round to a reasonable number of decimal places. In this case, rounding to two decimal places gives us a radius of r ≈ 28.01 cm. However, for most purposes, we can simply round to the nearest whole number, resulting in r = 28 cm.
Therefore, the given circumference (176 cm) corresponds to a radius of 28 cm, validating the assertion.
