Question

lesson 6
using the relationship between a circle’s circumference and diameter

solve each problem. show your work.

1 what is the radius of the circle?
2 what is the circumference of the circle? write your answer using π.
3 the diameter of a circle is 10 yards. find the approximate circumference of the circle, using 3.14 for π.
4 the radius of a circle is 15 inches. what is the circumference of the circle? write your answer using π.
5 the diameter of a circle is 24 feet. what is the approximate circumference of the circle? use 3.14 for π.
6 what is the exact circumference of a circle with diameter 48 millimeters?
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grade 7 • lesson 6
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Explanation:

Step1: Recall radius - diameter relation

The radius $r$ of a circle is half of its diameter $d$, i.e., $r=\frac{d}{2}$.

Step2: For the first circle

If the diameter $d = 18$ ft, then $r=\frac{18}{2}=9$ ft.

Step3: Recall circumference formula

The formula for the circumference $C$ of a circle is $C = 2\pi r=\pi d$.

Step4: For the second circle

If the diameter $d = 10$ cm, then $C=\pi d = 10\pi$ cm.

Step5: For the third circle

Given $d = 10$ yards and $\pi\approx3.14$, then $C=\pi d\approx3.14\times10 = 31.4$ yards.

Step6: For the fourth circle

Given $r = 15$ inches, then $C = 2\pi r=2\pi\times15=30\pi$ inches.

Step7: For the fifth circle

Given $d = 24$ feet and $\pi\approx3.14$, then $C=\pi d\approx3.14\times24 = 75.36$ feet.

Step8: For the sixth circle

Given $d = 48$ millimeters, then $C=\pi d = 48\pi$ millimeters.

Answer:

1. 9 ft
2. $10\pi$ cm
3. 31.4 yards
4. $30\pi$ inches
5. 75.36 feet
6. $48\pi$ millimeters