Question

circumference
17.24 ft
15 in
31.34 cm
75.36 ft
find the radius
radius
diameter

Explanation:

Step1: Recall the formula for the circumference of a circle

$C = 2\pi r=\pi d$, where $C$ is the circumference, $r$ is the radius and $d$ is the diameter.

Step2: Solve for the radius when $C = 17.27$ ft

Since $C = 2\pi r$, then $r=\frac{C}{2\pi}$. Substituting $C = 17.27$ ft and $\pi\approx3.14$, we have $r=\frac{17.27}{2\times3.14}=\frac{17.27}{6.28}=2.75$ ft.

Step3: Solve for the diameter

Since $d = 2r$, when $r = 2.75$ ft, $d=2\times2.75 = 5.5$ ft.

Step4: Solve for the radius when $C = 31.34$ cm

$r=\frac{C}{2\pi}$, substituting $C = 31.34$ cm and $\pi\approx3.14$, $r=\frac{31.34}{2\times3.14}=\frac{31.34}{6.28}\approx5$ cm.

Step5: Solve for the diameter

$d = 2r$, when $r\approx5$ cm, $d = 10$ cm.

Step6: Solve for the radius when $C = 75.36$ ft

$r=\frac{C}{2\pi}$, substituting $C = 75.36$ ft and $\pi\approx3.14$, $r=\frac{75.36}{2\times3.14}=\frac{75.36}{6.28}=12$ ft.

Step7: Solve for the diameter

$d = 2r$, when $r = 12$ ft, $d = 24$ ft.

Step8: Solve for the radius when $C = 15$ in

$r=\frac{C}{2\pi}$, substituting $C = 15$ in and $\pi\approx3.14$, $r=\frac{15}{2\times3.14}=\frac{15}{6.28}\approx2.39$ in.

Step9: Solve for the diameter

$d = 2r$, when $r\approx2.39$ in, $d\approx4.78$ in.

Answer:

For $C = 17.27$ ft: radius is $2.75$ ft, diameter is $5.5$ ft.
For $C = 31.34$ cm: radius is approximately $5$ cm, diameter is $10$ cm.
For $C = 75.36$ ft: radius is $12$ ft, diameter is $24$ ft.
For $C = 15$ in: radius is approximately $2.39$ in, diameter is approximately $4.78$ in.