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

- Rhombus construction

Construct ABCD rhombus if its diagonal AC=9 cm and side AB = 6 cm. Inscribe a circle in it touching all sides... - The mast

A 40 m high mast is secured in half by eight ropes of 25 m long. The ends of the ropes are equidistant from each other. Calculate this distance. - Circle chord

What is the length d of the chord circle of diameter 58 mm, if distance from the center circle is 24 mm? - Clock

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

The rectangle is 28 cm long and 21 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 cm^{2.}Calculate the volume of a cone. - Rectangle

In rectangle with sides 10 and 9 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? - Circle arc

Circle segment has a circumference of 13.26 mm and 252.03 mm^{2}area. Calculate the radius of the circle and size of central angle. - Cylinders

Area of the side of two cylinders is same rectangle of 45 cm × 32 cm. Which cylinder has a larger volume and by how much? - Circles

The areas of the two circles are in the ratio 1:15. The larger circle has diameter 25. Calculate the radius of the smaller circle. - Gear

Two gears, fit into each other, has transfer 1:5. Centres of gears are spaced 28 cm. What are the radii of the gears? - Radians

Convert 54° to radians. Write result as multiple of number π. - 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. - Tangents

To circle with a radius of 98 dm from the point A guided two tangents. The distance of both points of contact is 155 dm. Calculate the distance from point A and circle centre. - Described

Calculate perimeter of the circle described by a triangle with sides 418, 59, 430. - Rhombus and inscribed

Rhombus has side a = 72 cm, the radius of the inscribed circle is r = 10 cm. Calculate the length of its two diagonals. - Rhombus

It is given a rhombus of side length a = 11 cm. Touch points of inscribed circle divided his sides into sections a_{1}= 6 cm and a_{2}= 5 cm. Calculate the radius r of the circle and the length of the diagonals of the rhombus. - Arc and segment

Calculate the length of circular arc l, area of the circular arc S_{1}and area of circular segment S_{2}. Radius of the circle is 49 and corresponding angle is ?. - 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? - Plastic pipe

Calculate weight of the plastic pipe with diameter d = 60 mm and length 400 cm if the wall thickness is 6 mm and the density of plastic is 1228 kg/m^{3.}

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