Answer :
To solve these problems, we'll use the formula for the circumference of a circle, which is given by:
[tex]C = 2 \pi r[/tex]
where [tex]C[/tex] is the circumference and [tex]r[/tex] is the radius of the circle.
3. Find the radius of a circle whose circumference is 176 cm.
Given the circumference [tex]C = 176[/tex] cm, we can rearrange the formula to solve for the radius [tex]r[/tex]:
[tex]r = \frac{C}{2\pi}[/tex]
Substitute the given circumference into the formula:
[tex]r = \frac{176}{2\pi}[/tex]
Using the approximation for [tex]\pi \approx 3.14[/tex], we get:
[tex]r = \frac{176}{2 \times 3.14}[/tex]
[tex]r \approx \frac{176}{6.28}[/tex]
[tex]r \approx 28[/tex] cm
Thus, the radius of the circle is approximately 28 cm. Among the given options, 14 cm or 35 cm, the correct answer is not listed. If the intention was to approximate using another more accurate value of [tex]\pi[/tex], ensure calculation accuracy!
4. Find the diameter of a wheel whose circumference is 264 cm.
The diameter [tex]d[/tex] of the circle can be found using:
[tex]d = \frac{C}{\pi}[/tex]
Given [tex]C = 264[/tex] cm and using [tex]\pi \approx 3.14[/tex], we have:
[tex]d = \frac{264}{3.14}[/tex]
[tex]d \approx 84.08[/tex] cm
So, the diameter of the wheel is approximately 84.08 cm. Again, ensure precision in the calculations if another value of [tex]\pi[/tex] was intended.
These calculations help you find the radius and diameter using the relationship between circumference and [tex]\pi[/tex].
