# 7th grade (12y) + circle - math problems

Find the radius of the circle with area S = 200 cm².
2. Coal mine
The towing wheel has a diameter of 1.7 meters. How many meters does the elevator cage lower when the wheel turns 32 times?
Calculate the radius of the circle whose length is 107 cm larger than its diameter
4. Hands
The clock shows 12 hours. After how many minutes will angle between the hour and minute hand 90°? Consider the continuous movement of both hands hours.
5. Rectangle
The rectangle is 21 cm long and 38 cm wide. Determine the radius of the circle circumscribing rectangle.
6. Washer
Washing machine drum wash at 58 RPM. Washing machine motor pulley has diameter 9 cm. What must be the diameter of the drum machine pulley when the motor is at 438 RPM?
7. Cylinders
Area of the side of two cylinders is same rectangle of 33 mm × 18 mm. Which cylinder has a larger volume and by how much?
8. Circle arc
Circle segment has a circumference of 135.26 dm and 2096.58 dm2 area. Calculate the radius of the circle and size of central angle.
9. Gear
Two gears, fit into each other, has transfer 2:3. Centres of gears are spaced 82 cm. What are the radii of the gears?
10. Cone
Circular cone of height 15 cm and volume 5699 cm3 is at one-third of the height (measured from the bottom) cut by a plane parallel to the base. Calculate the radius and circumference of the circular cut.
11. Earth parallel
Earth's radius is 6370 km long. Calculate the length parallel of latitude 50°.
12. Arc
Circle arc corresponding to angle is 32° is 28 dm long. What is the length of the entire circle?
13. Quarter circular
The wire that is hooked around the perimeter of quarter-circular arc has length 3π+12. Determine the radius of circle arc.
14. Cap
Jesters hat is shaped a rotating cone. Calculate how much paper is needed to the cap 60 cm high when head circumference is 52 cm.
15. Pizza
Pizza with a diameter 50 cm have weight 559 g. What diameter will have a pizza weighing 855 g if it is make from the same cloth (same thickness....) and same decorated?
16. Bicycle wheel
A bicycle wheel has a diameter of 60 cm. Approximately how many times does wheel rotate at 2.5 km long trip?
17. Circle
How big is area of circle if its circumference is 80.6 cm?
18. Cu wire
Copper wire has a length l = 980 m and diameter d = 8 mm. Calculate the weight if density of copper is ρ = 8500 kg/m3. Result round to one decimal place.