Circle - practice for 13 year olds - page 22 of 29
Number of problems found: 563
- Annulus from triangle
Calculate the area of the area bounded by a circle circumscribed and a circle inscribed by a triangle with sides a = 25 mm, b = 29 mm, c = 36 mm. - Rhombus construction
Construct ABCD rhombus if its diagonal AC=9 cm and side AB = 6 cm. Inscribe a circle in it, touching all sides. - Pentagonal prism
The regular pentagonal prism is 10 cm high. The radius of the circle of the described base is 8 cm. Calculate the volume and surface area of the prism. - Concentric circles
A circle K with radius r = 8 cm is given. What radius must a smaller concentric circle have to divide circle K into two parts of equal area? - Concentric circle construction
Construct three concentric circles k, l, m with center at point S and with radii 2 cm, 3 cm, and 40 mm - 6 regular polygon
A regular six-sided polygon has a side 5 cm long. Calculate its area. Compare how many more cm² (square centimeters) has a circle inscribed the 6-gon. - Triangle construction
Construct triangle KLM if side m=6.5 cm, median to the side m tm=4 cm, height to side m: vm=3.2 cm - Trisection of a line segment
Divide the line segment AB into three equal parts. Instructions: Construct an equilateral triangle ABC and find its center (e.g., the described circles). - Lawns
Before a sports hall are two equally large rectangular lawns measuring 40 m and 12 m. Maintenance of a 10 m² lawn costs 45 CZK yearly. On each lawn is a circular flowerbed with a diameter of 8 meters. How much money is needed each year to take on lawn car - Clock face
On the circular face of the clock, we connect the points corresponding to the numbers 2, 5, and 9 to each other, which creates a triangle. Calculate the sizes of all interior angles. - Construct rhombus
Construct rhombus ABCD if given diagonal length | AC | = 8 cm, inscribed circle radius r = 1.5 cm - Annulus outer radius
An annulus with an area S = 4.2 square meters has an inner radius r = 2.25 m. Determine the outer radius of the annulus. - Octagon area
An irregular convex octagon is inscribed in the circle. Its four adjacent sides have a length of 3, and the remaining four adjacent sides have a size of 2. What is the area of a given octagon? - Trapezoid - construction
Construct a trapezoid KLMN, where: k = 9 cm, l = 4 cm, m = 5 cm and angle α = 45° - Plastic pipe
Calculate the plastic pipe's weight with diameter d = 100 mm and length 330 cm if the wall thickness is 4 mm and the density of plastic is 1346 kg/m³. - Two chords
Two parallel chords are drawn in a circle with a radius r = 26 cm. One chord has a length of t1 = 48 cm, and the second has a length of t2 = 20 cm, with the center lying between them. Calculate the distance between two chords. - Quadrilateral construction
Construct a quadrilateral ABCD with dimensions AB, BC, AC, BD, and angle d = CDA. - Two chords
Calculate the length of chord AB and perpendicular chord BC to the circle if AB is 4 cm from the circle's center and BC 8 cm from the center. - Circle chord distance
The figure shows the circles k₁(S₁; r1=9 cm) and k₂(S2; r2 = 5 cm). Their intersections determine a common chord t 8 cm long. Calculate the center distance |S₁ S₂| in cm to two decimal places. - Hexagon Area from Radius
Calculate the area of a regular hexagon if the radius of the circle circumscribed is 6.8 cm.
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