Circle + expression of a variable from the formula - math problems
- 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.
- 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 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?
- What is bigger?
Which ball has a larger volume: a football with a circumference of 66 cm or a volleyball with a diameter of 20 cm?
- The Earth
The Earth's surface is 510,000,000 km2. Calculates the radius, equator length, and volume of the Earth, assuming the Earth has the shape of a sphere.
- A cell tower
A cell tower is located at coordinates (-5, -7) and has a circular range of 12 units. If Mr. XYZ is located at coordinates (4,5), will he be able to get a signal?
- 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.
- The bridge
A vehicle weighing 5,800 kg passes 41 km/h on an arched bridge with a radius of curvature of 62 m. What force is pushing the car onto the bridge as it passes through the center? What is the maximum speed it can cross over the center of the bridge so that
- 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?
- Perimeter of the circle
Calculate the perimeter of the circle in dm, whose radius equals the side of the square containing 0.49 dm2?
- 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?
- Inscribed circle
A circle is inscribed at the bottom wall of the cube with an edge (a = 1). What is the radius of the spherical surface that contains this circle and one of the vertex of the top cube base?
- Circular railway
The railway is to interconnect in a circular arc the points A, B, and C, whose distances are | AB | = 30 km, AC = 95 km, BC | = 70 km. How long will the track from A to C?
We enlarge the circular flower bed, so its radius increased by 3 m. The substrate consumption per enlarged flower bed was (at the same layer height as before magnification) nine times greater than before. Determine the original flowerbed radius.
Find the radius of the circle with area S = 200 cm².
- Cylinder and its circumference
If the height of a cylinder is 4 times its circumference c, what is the volume of the cylinder in terms of its circumference, c?
- Folding table
The folding kitchen table has a rectangular shape with an area of 168dm2 (side and is 14 dm long). If necessary, it can be enlarged by sliding two semi-circular plates (at sides b). How much percent will the table area increase? The result round to one-hu
- Two chords
Calculate the length of chord AB and perpendicular chord BC to circle if AB is 4 cm from the center of the circle and BC 8 cm from the center of the circle.
- Radius of the circle
Calculate the radius of the circle whose length is 107 cm larger than its diameter
- Steel tube
The steel tube has an inner diameter of 4 cm and an outer diameter of 4.8 cm. The density of the steel is 7800 kg/m3. Calculate its length if it weighs 15 kg.