Question

the radius, r cm, of a circle is given as 9 cm, correct to the nearest whole number. (a) write down the limits between which r must lie. (b) calculate the least possible circumference of the circle, giving your answer in terms of π.

Explanation:

Step1: Determine lower and upper bounds

When a value is given correct to the nearest whole number, if the value is $n$ (in this case $n = 9$), the lower - bound is $n - 0.5$ and the upper - bound is $n+0.5$. So, the radius $r$ satisfies $8.5\leq r<9.5$.

Step2: Recall the formula for the circumference of a circle

The formula for the circumference of a circle is $C = 2\pi r$.

Step3: Find the least possible circumference

To find the least possible circumference, we use the least possible value of the radius. The least possible value of $r$ is $8.5$ cm. Substitute $r = 8.5$ into the formula $C = 2\pi r$. We get $C=2\pi\times8.5 = 17\pi$ cm.

Answer:

(a) $8.5\leq r<9.5$
(b) $17\pi$ cm