Question

Find the radius and diameter of a circle with the following circumferences. If you need to, use 3 for π.

C = 30 inches
C = 37.5 inches
C = 50π cm
C = 26π cm
C = 18.6 ft

Answer 1

Answer on Question #58083 – Math – Geometry

Question

Find the radius and diameter of a circle with the following circumferences. If you need to, use 3 for $\pi$.

a) $C = 30$ inches

b) $C = 37.5$ inches

c) $C = 50\pi$ cm

d) $C = 26\pi$ cm

e) $C = 18.6$ ft

Solution

From a well-known formula for circumference of circle

$$C = 2\pi R = \pi D$$

where $R =$ radius of circle, $D =$ diameter,

we can get

$$D = \frac{C}{\pi}; R = \frac{C}{2\pi}$$

Next,

a)

$$D = \frac{C}{\pi} = \frac{30}{3} = 10 \text{ inches}; R = \frac{C}{2\pi} = \frac{30}{6} = 5 \text{ inches}$$

b)

$$D = \frac{C}{\pi} = \frac{37.5}{3} = 12.5 \text{ inches}; R = \frac{C}{2\pi} = \frac{37.5}{6} = 6.25 \text{ inches}$$

c)

$$D = \frac{C}{\pi} = \frac{50\pi}{\pi} = 50 \text{ cm}; R = \frac{C}{2\pi} = \frac{50\pi}{2\pi} = 25 \text{ cm}$$

d)

$$D = \frac{C}{\pi} = \frac{26\pi}{\pi} = 26 \text{ cm}; R = \frac{C}{2\pi} = \frac{26\pi}{2\pi} = 13 \text{ cm}$$

e)

$$D = \frac{C}{\pi} = \frac{18.6}{3} = 6.2 \text{ ft}; R = \frac{C}{2\pi} = \frac{18.6}{6} = 3.1 \text{ ft}$$

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