Practice problems of the circle - page 39 of 48
A circle is a geometric shape that consists of all points that are a fixed distance, called the radius, away from a central point called the center. The distance around the circle is called the circumference and the region enclosed by the circle is called the area of the circle. The formula for the circumference of a circle is C = 2πr, where C is the circumference, r is the radius, and π is a mathematical constant, the Ludolph number, approximately equal to 3.1415926.The formula for the area of a circle is A = πr2, where A is the area and r is the radius.
The diameter of a circle is a line segment that passes through the center of the circle and has its endpoints on the circle. It is the longest distance across the circle and is also twice the length of the radius. The formula for the diameter of a circle is d = 2 * r, where d is the diameter and r is the radius. The diameter of a circle is an important measurement in geometry and is used in many mathematical formulas, such as the formula for the circumference of a circle (C = πd)
Number of problems found: 948
- Round table tablecloth
The round table has an area of 50.24 dm². Calculate the circular tablecloth diameter if it extends beyond the table's edge by 30 cm. - Determine 54881
On the tourist map with a scale of 1:50000, the section of the railway line between Bobrová Lhota and Javořiště is replaced by an arc of a circle with a radius of 6 cm. The arc is 90°. Determine the actual length of the track between the two villages. - Hexagon
Draw a regular hexagon inscribed in a circle with a radius r=8 cm. What is its perimeter? - Hexagonal 8200
The tops of the base of a regular hexagonal pyramid lie on a circle with a radius of 10 cm. The height of the pyramid is 12cm. What is its volume?
- Calculate 80636
Calculate the distance of a chord 19 cm long from the center of a circle with a diameter of 28 cm. - Construction 55311
Construct a KLM triangle where side k is 6.7 cm, the line to the k side is 4.1 cm, and the LKM angle is 63 degrees. Write the construction procedure. - Construct 13581
The vertices of the triangle ABC lie on the circle k. The circle k is divided into three parts in a ratio of 1:2:3. Construct this triangle. - Outside tangents
Calculate the length of the line segment S1S2 if the circles k1 (S1, 8cm) and k2 (S2,4cm) touch the outside. - 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 square's side and the circle's arc. What is the ratio of the areas of the large and small squares?
- Rectangle - parallelogram
A rectangle is circumscribed by a circle with a radius of 5 cm. The short side of the rectangle measures 6 cm. Calculate the perimeter of a parallelogram ABCD, whose vertices are the midpoints of the sides of the rectangle. - Rhombus construction
Construct ABCD rhombus if its diagonal AC=9 cm and side AB = 6 cm. Inscribe a circle in it, touching all sides. - Calculate 2577
Calculate the length of the circle chord, which is 2.5 cm from the circle's center. The radius is 6.5 cm. - Horizontal 83148
The bend has a radius of r = 100 m and is inclined at an angle of 20° to the horizontal plane (= tilt angle). What is the safe (the "best") speed to go through this curve? Sketch the picture regarding NIVS, mark the forces, and calculate. - Deformation 6260
The carpet is wound on a cardboard roll in the shape of a cylinder with a diameter of d=12cm and a length of l=2m. The rolled-up carpet has an outer diameter of D=38cm, and the thickness of the rug is 8mm. What area can the carpet cover after unfolding? D
- Construction: 81894
Construct a rhombus that has a side length of 5 cm and a height of 4.5 cm. Outline: Analysis: Construction: Method: - From plasticine
Michael modeled from plasticine a 15 cm high pyramid with a rectangular base with the sides of the base a = 12 cm and b = 8 cm. From this pyramid, Janka modeled a rotating cone with a base diameter d = 10 cm. How tall was Janka's cone? - Sphere in cone
A sphere is inscribed in the cone (the intersection of their boundaries consists of a circle and one point). The ratio of the ball's surface and the area of the base is 4:3. A plane passing through the axis of a cone cuts the cone in an isosceles triangle - Circle from string
Martin has a long 628 mm string. He makes a circle from it. Calculate the radius of the circle. - Chord MN
Chord MN of the circle has distance from the center circle S 120 cm. Angle MSN is 64°. Determine the radius of the circle.
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