Sphere practice problems - page 9 of 12
Number of problems found: 231
- Elevation
What must be an observer's elevation so that he may see an object on the Earth 866 km away? Assume the Earth to be a smooth sphere with a radius 6378.1 km. - Sphere cube filling
Nine identical spheres are stacked in the cube to fill the cube's volume as much as possible. What part of the volume will the cube fill? - Cathedral roof sphere
Cathedral height is 110 m, sphere weight 6000 kg, dome diameter 43 m, crane arm length 25 m a) what was the diameter of this sphere? b) how much mechanical work had to be done to lift it to the designated place? - Tropics and polar zones
What percentage of the Earth's surface lies in the tropical, temperate, and polar zones? Tropics border individual zones at 23°27' and polar circles at 66°33'. - The roof
The roof has a spherical canopy with a base diameter of 8 m and a height of 2 m. Calculate the foil area with which the roof is covered when calculating 13% for waste and residues. - Spherical cap
From the sphere with a radius of 26 was a truncated spherical cap. Its height is 2. What part of the volume is a spherical cap from the whole sphere? - Pebble
The aquarium is filled with two-thirds water with internal dimensions of the bottom 40 cm × 35 cm and a height of 30 cm. Calculate how many millimeters the water level in the aquarium rises by dipping a pebble-shaped sphere with a diameter of 18 cm. - Sphere - parts
Calculate the area of a spherical cap, which is part of an area with a base radius ρ = 8 cm and a height v = 4.2 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? - Reservoir - spherical
The reservoir is a sphere with a diameter of 12 m. If it is painted twice, how many kg of paint is needed to paint it, and one kilogram is enough to paint about 8m²? - Inscribed cube
A cube is inscribed in a sphere with a radius of 27 cm. Calculate its volume and surface area. - Above Earth
To what height must a boy be raised above the earth to see one-fifth of its surface? - Airplane
Aviator sees part of the earth's surface with an area of 200,000 square kilometers. How high does he fly? - Two Sections
A sphere with a radius of 5 cm was divided into two spherical caps. The height of the smaller cap is 1 cm. Determine the volume of the smaller cap to the nearest hundredth of a cm³. - Spherical tank
The water tower tank is a sphere with a radius of 35ft. If the tank is filled to one-quarter full, what is the height of the water? - Ball screen
The diameter of the ball screen is 30 cm. If we add 5% of the material to be sewn, how many m² of fabric do we need to make? - Spherical cap
The spherical cap has a base radius of 8 cm and a height of 5 cm. Calculate the radius of a sphere of which this spherical cap is cut. - Balloon fabric calculation
How much fabric is needed to sew a spherical hot air balloon with a diameter of 15 m? How much air is needed to inflate the balloon? - Cone sphere volume
A sphere is inscribed in an equilateral cone with a base diameter of 12 cm. Calculate the volume of both bodies. What percentage of the volume of the cone is filled by the inscribed sphere? - Martians
A sphere-shaped spaceship with a diameter of 6 m landed in the meadow. To avoid attracting 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?
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