# Ratio + circle - math problems

On solving problems and tasks with proportionally, we recommend hint rule of three. Rule of three (proportionality) help solve examples of direct and inverse proportionality. Three members make possible to calculate the fourth - unknown member.

1. Ratio of sides Calculate the area of a circle that has the same circumference as the circumference of the rectangle inscribed with a circle with a radius of r 9 cm so that its sides are in ratio 2 to 7.
2. Ratio of volumes If the heights of two cylindrical drums are in the ratio 7:8 and their base radii are in the ratio 4:3. What is the ratio of their volumes?
3. Three segments The circle is divided into 3 segments. Segment A occupies 1/4 of the area, segment B occupies 1/3 of the area. What part is occupied by section C? In what proportion are areas A: B: C?
4. A large A large gear will be used to turn a smaller gear. The large gear will make 75 revolutions per minute. The smaller gear must make 384 revolutions per minute. Find the smallest number of teeth each gear could have. [Hint: Use either GCF or LCM. ]
5. Three shapes 1/5 of a circle is shaded. The ratio of area if square to the sum of area of rectangle and that of the circle is 1:2. 60% of the square is shaded and 1/3 of the rectangle is shaded. What is the ratio of the area of circle to that of the rectangle?
6. Arc What area of a circle occupied the flowers planted in the arc of a circle with radius 4 m with central angle 45°?
7. Wheels Small tractor wheel with a diameter of 60 cm must be rotated 8 times to overcome some pathway. How many times must turn the big tractor wheel with a radius 60 cm to overcome the same distance?
8. Rectangle - desc circle Length of the sides of the rectangle are at a ratio 1: 3 . Radius of the circle circumscribed to rectangle is 10 cm. Calculate the rectangle's perimeter.
9. Clock What distance will pass end of 8 cm long hour hand for 15 minutes?
10. Velocity ratio Determine the ratio at which the fluid velocity in different parts of the pipeline (one part has a diameter of 5 cm and the other has a diameter of 3 cm), when you know that at every point of the liquid is the product of the area of tube [S] and the fluid.
11. Axial section Axial section of the cylinder has a diagonal 40 cm. The size of the shell and the base surface are in the ratio 3:2. Calculate the volume and surface area of this cylinder.
12. 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?
13. 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?
14. Arc The length of the circle is 41 amd arc length of the circle 9. What is the magnitude of the angle of this arc?
15. Triangle in circle Vertices of the triangle ABC lies on a circle with radius 3 so that it is divided into three parts in the ratio 4:4:4. Calculate the circumference of the triangle ABC.
16. Pipeline How much percent has changed (reduced) area of pipe cross-section, if circular shape changed to square with same perimeter?
17. Circles The areas of the two circles are in the ratio 2:20. The larger circle has diameter 20. Calculate the radius of the smaller circle.
18. Circumferential angle Vertices of the triangle ΔABC lies on circle and divided it into arcs in the ratio 2:2:9. Determine the size of the angles of the triangle ΔABC.
19. Axial section Axial section of the cylinder has a diagonal 31 cm long and we know that the area of the side and the area of base is in ratio 3:2. Calculate the height and radius of the cylinder base.
20. Circumference - a simple What is the ratio of the circumference of any circle and its diameter? Write the result as a real number rounded to 2 decimal places.

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