To find the diameter of a circle given its circumference and the value of [tex]\(\pi\)[/tex], we can use the formula for the circumference of a circle:
[tex]\[ C = \pi d \][/tex]
where [tex]\( C \)[/tex] is the circumference of the circle, [tex]\( \pi \)[/tex] is pi, and [tex]\( d \)[/tex] is the diameter.
Given:
- The circumference [tex]\( C \)[/tex] is 66 cm.
- The value of [tex]\( \pi \)[/tex] is [tex]\(\frac{22}{7}\)[/tex].
We need to find the diameter [tex]\( d \)[/tex]. Rearranging the formula for the diameter, we get:
[tex]\[ d = \frac{C}{\pi} \][/tex]
Substitute the given values into the formula:
[tex]\[ d = \frac{66}{\frac{22}{7}} \][/tex]
When dividing by a fraction, it is equivalent to multiplying by its reciprocal. So we can rewrite it as:
[tex]\[
d = 66 \times \frac{7}{22}
\][/tex]
Next, we simplify the fraction [tex]\(\frac{7}{22}\)[/tex]:
[tex]\[
d = 66 \times \frac{7}{22} \rightarrow d = 66 \times \frac{1}{\frac{22}{7}} \rightarrow d = 66 \times \frac{7}{22} \rightarrow d = 66 \times \frac{1}{\frac{22}{7}} \rightarrow d = 66 \times \frac{7}{22} \rightarrow d = 66 \times 0.3181 \approx 21 \text{ cm}
\][/tex]
\]
Hence:
[tex]\[ d = 21 \][/tex]
Therefore, the diameter of the circle is 21 cm.
The correct answer is:
B. 21 cm
