Circle - 9th grade (14y) - math problems
Number of problems found: 250
- 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.
- Concentric circles and chord
In a circle with a diameter d = 10 cm, a chord with a length of 6 cm is constructed. What radius have the concentric circle while touch this chord?
Calculate the size of the smaller of the angles determined by lines A1 A4 and A2 A10 in the regular dodecagon A1A2A3. .. A12. Express the result in degrees.
- 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?
- 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.
- Round flowerbed
Around a round flowerbed with a diameter of 6 meters and I will make a sidewalk up to 0.5 meters wide. How much gravel is needed if the layer is to be 5 cm high?
- Annulus from triangle
Calculate the content of the area bounded by a circle circumscribed and a circle inscribed by a triangle with sides a = 25mm, b = 29mm, c = 36mm
- Hexa pyramid
The base of the regular pyramid is a hexagon, which can be described by a circle with a radius of 1 m. Find the volume of the pyramid 2.5 m high.
- 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.
- The Indian tent
The Indian tent is cone-shaped. Its height is 3.5 m. The diameter of the base is 2.5 m. How much canvas is needed to make a tire?
- 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 circles
Two circles with the same radius r = 1 are given. The center of the second circle lies on the circumference of the first. What is the area of a square inscribed in the intersection of given circles?
Two concentric circles with radii 1 and 9 surround the annular circle. This ring is inscribed with n circles that do not overlap. Determine the highest possible value of n.
- Hexagonal pyramid
Calculate the surface area of a regular hexagonal pyramid with a base inscribed in a circle with a radius of 8 cm and a height of 20 cm.
- Rotaty motion
What is the minimum speed and frequency that we need to rotate with water can in a vertical plane along a circle with a radius of 70 cm to prevent water from spilling?
- Eq triangle minus arcs
In an equilateral triangle with a 2cm side, the arcs of three circles are drawn from the centers at the vertices and radii 1cm. Calculate the content of the shaded part - a formation that makes up the difference between the triangle area and circular cuts
- Tree trunk
What is the smallest diameter of a tree trunk that we can cut a square-section square with a side length of 20 cm?
Calculate the side a, the circumference and the area of the regular 5-angle if Rop = 6cm.
- Two chords
In a circle with radius r = 26 cm two parallel chords are drawn. One chord has a length t1 = 48 cm and the second has a length t2 = 20 cm, with the center lying between them. Calculate the distance of two chords.