Circle - 9th grade (14y) - examples
- Spherical cap 4
What is the surface area of a spherical cap, the base diameter 20 m, height 2.5 m? Calculate using formula.
- 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. ]
- Circle chord
What is the length d of the chord circle of diameter 36 m, if distance from the center circle is 16 m?
The rectangle is 11 cm long and 45 cm wide. Determine the radius of the circle circumscribing rectangle.
How many times a day hands on a clock overlap?
- Cone A2V
Surface of cone in the plane is a circular arc with central angle of 126° and area 415 cm2. Calculate the volume of a cone.
In rectangle with sides 10 and 8 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?
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.
- 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.
Area of the side of two cylinders is same rectangle of 50 cm × 11 cm. Which cylinder has a larger volume and by how much?
- Circle arc
Circle segment has a circumference of 72.95 cm and 1386.14 cm2 area. Calculate the radius of the circle and size of central angle.
It is given a rhombus of side length a = 29 cm. Touch points of inscribed circle divided his sides into sections a1 = 14 cm and a2 = 15 cm. Calculate the radius r of the circle and the length of the diagonals of the rhombus.
- Rhombus and inscribed circle
It is given a rhombus with side a = 6 cm and the radius of the inscribed circle r = 2 cm. Calculate the length of its two diagonals.
Two gears, fit into each other, has transfer 2:3. Centres of gears are spaced 82 cm. What are the radii of the gears?
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.
Convert 270° to radians. Write result as multiple of number π.
- 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?
Calculate perimeter of the circle described by a triangle with sides 478, 255, 352.
- Arc and segment
Calculate the length of circular arc l, area of the circular arc S1 and area of circular segment S2. Radius of the circle is 33 and corresponding angle is ?.
- Plastic pipe
Calculate weight of the plastic pipe with diameter d = 70 mm and length 380 cm if the wall thickness is 4 mm and the density of plastic is 1367 kg/m3.