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= 82=4 inches. To find the circumference, we will use the formula C=π d.

C=π d

Substitute

d= 8

C=π( 8)

RoundDec

Round to 1 decimal place(s)

C≈ 25.1

The circumference of the disc with diameter 8 inches is around 25.1 inches. To find the area, we use the formula A=π r^2.

A=π r^2

Substitute

r= 4

A=π( 4)^2

Multiply

Multiply

A=16π

RoundDec

Round to 1 decimal place(s)

A≈ 50.3

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= 102=5 inches. To find the circumference, we use the formula C=π d.

C=π d

Substitute

d= 10

C=π( 10)

RoundDec

Round to 1 decimal place(s)

C≈ 31.4

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=π r^2.

A=π r^2

Substitute

r= 5

A=π( 5)^2

Multiply

Multiply

A=25π

RoundDec

Round to 1 decimal place(s)

A≈ 78.5

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
8in	≈ 25.1in	≈ 50.3in^2
10in	≈ 31.4in	≈ 78.5in^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.