Exercise 33 Page 63

Both the area and the circumference of a circle increase as the diameter increases. To find the range of possible sizes of the flying disc, we need to find the circumference and area of the discs with the smallest and the largest possible diameter. Remember, the radius is half of the diameter. We need to remember this, since the area of a circle is usually expressed in terms of the radius.

Disc with diameter $8$ inches.

If the diameter is $d=8$ inches, then the radius is $r=\frac{8}{2}=4$ inches. To find the circumference, we will use the formula $C=\pi d.$ The circumference of the disc with diameter $8$ inches is around $25.1$ inches. To find the area, we use the formula $A=\pi r^2.$ The area of the disc with a diameter of $8$ inches is around $50.3$ square inches.

Disc with diameter $10$ inches.

If the diameter is $d=10$ inches, then the radius is $r=\frac{10}{2}=5$ inches. To find the circumference, we use the formula $C=\pi d.$ The circumference of the disc with a diameter of $10$ inches is around $31.4$ inches. To find the area, we use the formula $A=\pi r^2.$ The area of the disc with a diameter of $10$ inches is around $78.5$ square inches.

Conclusion

Here is the summary of our results.

Diameter	Circumference	Area
$8\text{ in}$	$\approx 25.1\text{ in}$	$\approx 50.3{\text{ in}}^2$
$10\text{ in}$	$\approx 31.4\text{ in}$	$\approx 78.5{\text{ in}}^2$

We can read the answer to the question from the table.

• The circumference of the flying discs is between $25.1$ and $31.4$ inches.
• The area of the flying discs is between $50.3$ and $78.5$ square inches.