Question

The radius, diameter, or circumference of a circle is given. Find the missing measures. Round to the nearest hundredth if necessary.

c= 19.6km, d=?km, r=?

a) d= 6.23km
b) d= 12.46km
c) d= 3.14km
d) d= 19.6km

r=?

a) r=1.57km
b) r= 9.8km
c) r= 0.78km
d) r= 19.6km

Answer 1

The circumference of a circle is given as 19.6 km. The correct diameter, calculated using the formula C = πd, is approximately 6.24 km, and the radius, which is half of the diameter, is approximately 3.12 km.

Step-by-step explanation:

The student has been given the circumference (C) of a circle and is instructed to find both the diameter (d) and the radius (r) of the circle. The circumference of a circle is related to the diameter and the radius as follows:

• Circumference (C) = π x diameter (d)
• Diameter (d) = 2 x radius (r)

Since C = 19.6 km is given, we use the formula for circumference to find the diameter:

1. d = C / π
2. d = 19.6 / 3.14159
3. d = 6.24 km (rounded to the nearest hundredth)

So, the diameter of the circle is approximately 6.24 km, which means answer b) d= 12.46km is incorrect and the correct answer is b) d= 6.24km.

To find the radius, we use the diameter:

1. r = d / 2
2. r = 6.24 / 2
3. r = 3.12 km (rounded to the nearest hundredth)

The correct radius of the circle is approximately 3.12 km, which means answer b) r= 9.8km is incorrect and the correct answer is c) r= 3.12km. Note: The options provided for the radius and diameter do not match this calculation, hence the correct answer in terms of the provided options would be a) r=1.57km and a) d= 6.23km respectively, despite being very slightly off from the calculated value. This is likely due to rounding differences.