Answer: The radius of the circle rounded to the nearest integer is 11 cm
Explanation:
To resolve this issue we can utilize the properties inherent to circles along with Pythagoras' theorem while denoting our circle's radius as "r".
Given that we know of a chord of length equaling up to 18 cm placed at a distance measuring exactly 6.3 cm away from the center of our circle sketching out a diagram would make it easier for us to visualize such a situation. Once visualizing this problem statement through our aforementioned diagram we may approach it using Pythagoras' theorem and examine the components regarding the right-angled triangle formed by half-length chord radius "r" and distance between center and chord respectively.
Our calculations factor in measurements representing half of our chords length (which is equal to precisely 9cm) alongside distances measuring up to exactly 6.3cm while possessing "r" on one end as shown below:
r^2 = (6.3cm)^2 + (9cm)^2
Simplifying said equation leads us to have:
r^2 =39.69cm^2+81cm^2
r²=120.69cm²
Calculating square roots on both sides leads us towards the approximation of r equaling around:
r ≈ √120.69cm²
r ≈10.99cm
Therefore rounding off R towards its nearest whole number would give us R=11cm in this case scenario.