8E Area of a Circle using Pi
Name______________________________________
1. What is π?
2. How do we use π?
3. A bicycle mechanic wants to put a strip of plastic between
the tube and tire of a 26-in. diameter bicycle tire. To the
nearest inch, how long should the strip of plastic be?
4. The most common tire size circumference is 67 inches. To
the nearest tenth, what is the length of the radius of the tire?
5. The diameter of a basketball rim is 18 in. A standard
basketball has a circumference of 30 in. About how much
room is there between the ball and the rim in a shot in which
the ball goes exactly in the center of the rim?
6. Three tennis balls are packaged in a pressurized can, one
on top of the other. Is height of the can or its circumference
greater? Justify your answer.
7. A circle is inscribed in a square with a side of 12 ft. What is
the area of the region between the square and the circle?
8. A square with a side of 12 ft is inscribed in a circle. What is
the area of the region between the square and the circle?
9. A square with a diagonal of 10 ft is inscribed in a circle.
What is the area of the region between the square and the
circle?
10. A circle is inscribed in a square with a diagonal of 12 ft.
What is the area of the region between the square and the
circle?
11. What is the area of the shaded region?
12. What is the area of the shaded region?
13. What is the area of the shaded region?
14. What is the area of the shaded region?
15. What is the area of the shaded region?
16. Triangle ABC is inscribed in circle O. Angle C is a right
angle, and AB=6. What is the area of the region inside the
circle but outside the triangle? Draw and label a diagram and
show all of your work.
17. You win if you throw a ball in the part of the board that is
shaded blue. Should you play the game?
18. In the figure, a square is
inscribed in a circle with
diameter d. What is the sum of
the areas of the shaded
regions, in terms of d?
æ
æ p 1ö
1ö
2 p
B. d 2 ç - ÷
A. d ç - ÷
è 4 2ø
è 4 4ø
æ
1ö
2 p
D. d 2 p -2
C. d ç - ÷
2
2
è
ø
E. d 2 p -1
( )
( )
19. The target is 10 feet in diameter. The inside 50-point circle is 2 feet in diameter.
Each ring is 1 foot wide. Point values for each ring are listed.
a. What is the area of the bull’s-eye?
b. What proportion of the area of the target is the bull’s-eye?
c. What is the area of the 10-point ring?
d. What is the total area of all of the shaded rings (including the bull’s-eye)?
e. What proportion of the area of the target is shaded?
f. What proportion of the area of the target is not shaded?
g. Is an archer more likely to score 40 points with two arrows by scoring 10 first
and 30 second or by scoring 20 points with both arrows? Explain your reasoning.