# Circle - 9th grade (14y) - examples

- Hypotenuse - RT

A triangle has a hypotenuse of 55 and an altitude to the hypotenuse of 33. What is the area of the triangle? - A cylinder

A cylinder 108 cm high has a circumference of 24 cm. A string makes exactly 6 complete turns around the cylinder while its two ends touch the cylinder's top and bottom. (forming a spiral around the cylinder). How long is the string in cm? - A bridge

A bridge over a river is in the shape of the arc of a circle with each base of the bridge at the river's edge. At the center of the river, the bridge is 10 feet above the water. At 27 feet from the edge of the river, the bridge is 9 feet above the water. H - Ruler and compass

Use a ruler and compass to construct a triangle ABC with AB 5cm BAC 60° and ACB 45°. - Circle chord

What is the length d of the chord circle of diameter 36 m, if distance from the center circle is 16 m? - Clock

How many times a day hands on a clock overlap? - Rectangle

The rectangle is 31 cm long and 28 cm wide. Determine the radius of the circle circumscribing rectangle. - Cone A2V

Surface of cone in the plane is a circular arc with central angle of 126° and area 415 dm^{2.}Calculate the volume of a cone. - Rectangle

In rectangle with sides 3 and 10 mark the diagonal. What is the probability that a randomly selected point within the rectangle is closer to the diagonal than to any side of the rectangle? - Circles

The areas of the two circles are in the ratio 2:14. The larger circle has diameter 14. Calculate the radius of the smaller circle. - Cylinders

Area of the side of two cylinders is same rectangle of 12 mm × 19 mm. Which cylinder has a larger volume and by how much? - Circle arc

Circle segment has a circumference of 41.89 m and 251.33 m^{2}area. Calculate the radius of the circle and size of central angle. - MO SK/CZ Z9–I–3

John had the ball that rolled into the pool and it swam in the water. Its highest point was 2 cm above the surface. Diameter of circle that marked the water level on the surface of the ball was 8 cm. Determine the diameter of John ball. - 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? - Rhombus

It is given a rhombus of side length a = 29 cm. Touch points of inscribed circle divided his sides into sections a_{1}= 14 cm and a_{2}= 15 cm. Calculate the radius r of the circle and the length of the diagonals of the rhombus. - Radians

Convert 270° to radians. Write result as multiple of number π. - Tangents

To circle with a radius of 41 cm from the point R guided two tangents. The distance of both points of contact is 16 cm. Calculate the distance from point R and circle centre. - Rhombus and inscribed

Rhombus has side a = 42 cm, the radius of the inscribed circle is r = 18 cm. Calculate the length of its two diagonals. - Described

Calculate perimeter of the circle described by a triangle with sides 478, 255, 352. - Circular pool

The base of pool is circle with a radius r = 10 m excluding circular segment that determines chord length 10 meters. Pool depth is h = 2m. How many hectoliters of water can fit into the pool?

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