Pythagorean theorem + sphere - practice problems
Number of problems found: 35
- Billiard balls
A layer of ivory billiard balls of radius 6.35 cm is in the form of a square. The balls are arranged so that each ball is tangent to every one adjacent to it. In the spaces between sets of 4 adjacent balls other balls rest, equal in size to the original.
- Float boya
A 0.5 meter spherical float is used as a location mark for a fishing boat anchor. It floats in salt water. Find the depth to which the float sinks if the material of which the float is made weighs 8 kilograms per cubic meter and salt water weighs 1027 kg/
- MO SK/CZ Z9–I–3
John had the ball that rolled into the pool, and it swam in the water. Its highest point was 2 cm above the surface. The diameter of the circle that marked the water level on the surface of the ball was 8 cm. Find the diameter of John ball.
One cube is an inscribed sphere and the other one described. Calculate the difference of volumes of cubes, if the difference of surfaces in 231 cm².
- Cube in a sphere
The cube is inscribed in a sphere with a volume 7253 cm³. Determine the length of the edges of a cube.
- What percentage
What percentage of the Earth’s surface is seen by an astronaut from a height of h = 350 km. Take the Earth as a sphere with the radius R = 6370 km
A sphere-shaped spaceship with a diameter of 6 m landed in the meadow. In order not to attract attention, the Martians covered it with a roof in the shape of a regular cone. How high will this roof be so that the consumption of roofing is minimal?
A domed stadium is in the shape of spherical segment with a base radius of 150 m. The dome must contain a volume of 3500000 m³. Determine the height of the dome at its centre to the nearest tenth of a meter.
- The hemisphere
The hemisphere container is filled with water. What is the radius of the container when 10 liters of water pour from it when tilted 30 degrees?
- A spherical segment
The aspherical section, whose axial section has an angle of j = 120° in the center of the sphere, is part of a sphere with a radius r = 10 cm. Calculate the cut surface.
- Sphere parts, segment
A sphere with a diameter of 20.6 cm, the cut is a circle with a diameter of 16.2 cm. .What are the volume of the segment and the surface of the segment?
- Tangent spheres
A sphere with a radius of 1 m is placed in the corner of the room. What is the largest sphere size that fits into the corner behind it? Additional info: Two spheres are placed in a corner of a room. The spheres are each tangent to the walls and floor and
- Sphere and cone
Within the sphere of radius G = 33 cm inscribe the cone with the largest volume. What is that volume, and what are the dimensions of the cone?
- Spherical cap
Place a part of the sphere on a 4.6 cm cylinder so that the surface of this section is 20 cm². Determine the radius r of the sphere from which the spherical cap was cut.
Aviator sees part of the earth's surface with an area of 200,000 square kilometers. How high he flies?
- Two balls
Two balls, one 8cm in radius and the other 6cm in radius, are placed in a cylindrical plastic container 10cm in radius. Find the volume of water necessary to cover them.
- Cube from sphere
What largest surface area (in cm2) can have a cube that we cut out of a sphere with radius 43 cm?
- Sphere slices
Calculate the volume and surface of a sphere if the radii of parallel cut r1=31 cm, r2=92 cm, and its distance v=25 cm.
- Metal balls
Four metal balls with a diameter of 5 cm are placed in a measuring cylinder with an inner diameter of 10 cm. What is the smallest water volume to be poured into the cylinder so that all balls are below the water level?
What must be the elevation of an observer in order that he may be able to see an object on the earth 536 km away? Assume the earth to be a smooth sphere with radius 6378.1 km.
Pythagorean theorem is the base for the right triangle calculator. Pythagorean theorem - practice problems. Sphere practice problems.