IMO Practice Test — Circles (Basics)
6 Questions • 25 min • Olympiad level
25:00
Question 1 of 6
hard
A circular garden (radius=14m) has a 3.5m wide path outside it. Find the area of the path. (pi=22/7)
132 m^2
231 m^2
346.5 m^2
462 m^2
Explanation: Outer radius = 17.5m. Path area = pi(17.5^2 - 14^2) = (22/7)(306.25-196) = (22/7)(110.25) = 346.5 m^2.
Question 2 of 6
hard
A wire bent into a circle has area 154 cm^2. The same wire is bent into a square. Find the square's area. (pi=22/7)
100 cm^2
111 cm^2
121 cm^2
132 cm^2
Explanation: pi*r^2=154 => r=7cm. Circumference=44cm. Square side=44/4=11cm. Area=11^2=121cm^2.
Question 3 of 6
hard
A semicircle sits on top of a rectangle (width=14cm, height=10cm). Find the total perimeter. (pi=22/7)
42 cm
48 cm
56 cm
72 cm
Explanation: Perimeter = two heights + base + semicircle arc = 10+10+14+(22/7*7) = 34+22 = 56 cm.
Question 4 of 6
hard
A circular track has inner radius 35m and outer radius 42m. Find the area of the track. (pi=22/7)
924 m^2
1386 m^2
1694 m^2
2464 m^2
Explanation: Area = (22/7)(42^2 - 35^2) = (22/7)(1764-1225) = (22/7)(539) = 1694 m^2.
Question 5 of 6
hard
A pizza of radius 12 cm is cut into 8 equal slices. Find the area of one slice. (pi=3.14)
28.26 cm^2
36.52 cm^2
56.52 cm^2
75.36 cm^2
Explanation: Total area = 3.14 x 12^2 = 452.16 cm^2. One slice = 452.16/8 = 56.52 cm^2.
Question 6 of 6
hard
The minute hand of a clock is 10.5 cm long. How far does the tip travel in 45 minutes? (pi=22/7)
33 cm
44 cm
49.5 cm
66 cm
Explanation: 45 min = 3/4 of full rotation. Distance = (3/4) x 2 x (22/7) x 10.5 = (3/4) x 66 = 49.5 cm.