Circle - 9th grade (14y) - practice problems
Number of problems found: 294
- Radio radius
Two friends have shortwave radios with a range of 13 km. The first of them travels by train at a speed of 48 km per hour along a straight section of track, from which the second of the friends is 5 km away. How long will radio friends be allowed for both
- Coat of arms
The class created its own coat of arms, which had a shape composed of an isosceles trapezoid ABCD (shorter base is a = 4.5 cm long, longer 2a = 9 cm, trapezoid height 6 cm) and a semicircle with center S and diameter AB. The trapezoid was formed by three
- Regular octagon pad
You need to make a pad in the shape of a regular octagon with a side length of 4 cm. What is the minimum diameter of the circle-shaped semi-finished product from which we make the pad, and what will be the percentage of waste? (Round the results to 1 deci
- Circle inscribed
There is a triangle ABC and a circle inscribed in this triangle with radius 15. The point T is the point of contact of the inscribed circle with the side BC. What is the area of the triangle ABC if | BT | = 25 a | TC | = 26?
- The spinner
The spinner below is spun 12 times. It landed on I 4 times, II 7 times, and III 1 time. What is the difference between the experimental and theoretical probabilities of landing on the II?
- Wheel gear
A drive wheel of radius 2 is connected to a drive wheel of radius 1 by a pulley of length 17. What is the distance between the wheel axles?
Find the area of a regular dodecagon (n=12) if the radius of the circumscribed circle is 5 cm.
- Woman's day
We can easily make a heart for mothers for Woman's day by drawing two semicircles to the two upper sides of the square standing on their top. What is the radius of the circle circumscribed by this heart when the length of the side of the square is 1?
Megapizza will be divided among 100 people. First gets 1%, 2nd 2% of the remainder, 3rd 3% of the remainder, etc. Last 100th 100% of the remainder. Which person got the biggest portion?
- Metal washers
Metal washers with a diameter of 80 mm are cut from a strip of steel sheet with a width of 10 cm and a length of 2 m. Calculate the percentage of material waste if no material is lost when two adjacent circles meet.
- Rotary motion
Find the orbital time, rotational frequency, and angular rate of the second and minute hands on the watch.
- Right triangle
A circle with a radius of 5 cm is described in a right triangle with a 6 cm leg. What is the height at the hypotenuse of this triangle?
- Constant Angular Acceleration
The particle began to move from rest along a circle with a constant angular acceleration. After five cycles (n = 5), its angular velocity reached the value ω = 12 rad/s. Calculate the magnitude of the angular acceleration ε of this motion and the time int
- Five circles
On the line segment CD = 6 there are 5 circles with a radius one at regular intervals. Find the lengths of the lines AD, AF, AG, BD, and CE.
- Inscribed and described circle
Find the radii of a circle inscribed and circumscribed by a regular pentagon whose side measures 3 cm.
- Ratio of squares
A circle is given in which a square is inscribed. The smaller square is inscribed in a circular arc formed by the side of the square and the arc of the circle. What is the ratio of the areas of the large and small squares?
- Square and circles
The square in the picture has a side length of a = 20 cm. Circular arcs have centers at the vertices of the square. Calculate the areas of the colored unit. Express area using side a.
Calculate the content of a regular 15-sides polygon inscribed in a circle with radius r = 4. Express the result to two decimal places.
- Circle and square
An ABCD square with a side length of 100 mm is given. Calculate the radius of the circle that passes through the vertices B, C and the center of the side AD.
- Two parallel chords
In a circle 70 cm in diameter, two parallel chords are drawn so that the center of the circle lies between the chords. Calculate the distance of these chords if one of them is 42 cm long and the second 56 cm.
Circle practice problems. Examples for 9th grade.