Sphere + triangle - practice problems - page 2 of 3
Number of problems found: 44
- 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? - MO SK/CZ Z9–I–3
John had the ball that rolled into the pool and 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 ball's surface was 8 cm. Find the diameter of John's ball. - Determine 4876
The rotating cone has a height of 72 cm and an angle at the top of 72 °. Determine the volume of the sphere. - 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 a radius R = 6370 km.
- Felix
Calculate how much land Felix Baumgartner saw after jumping from 36 km above the ground. The radius of the Earth is R = 6378 km. - Tropical, mild and arctic
How many percent of the Earth's surface lies in the tropical, mild, and arctic ranges? The border between the ranges is the parallel 23°27' and 66°33'. - Elevation
What must be an observer's elevation so that he may see an object on the Earth 536 km away? Assume the Earth to be a smooth sphere with a radius 6378.1 km. - Intersection 40981
The intersection of a plane is 2 cm from the sphere's center, and this sphere is a circle whose radius is 6 cm. Calculate the surface area and volume of the sphere. - Tropics and polar zones
What percentage of the Earth's surface lies in the tropical, temperate, and polar zone? Tropics border individual zones at 23°27' and polar circles at 66°33'.
- Above Earth
To what height must a boy be raised above the earth to see one-fifth of its surface? - Sphere - parts
Calculate the area of a spherical cap, which is part of an area with a base radius ρ = 10 cm and a height v = 3.4 cm. - 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. - Airplane
Aviator sees part of the earth's surface with an area of 200,000 square kilometers. How high does he fly? - Pilot
How high is the airplane's pilot to see 0.001 of Earth's surface?
- Spherical cap
What is the surface area of a spherical cap, the base diameter 23 m, and height 3 m? - Spherical 63214
The gas tank consists of a 16m high cylinder with a diameter of 28m, which is closed at the top by a spherical canopy. The center of the spherical surface lies 4m below the bottom of the cylinder. Please calculate the spherical surface's radius and the ca - 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 we cut the spherical cap. - Calculate 81034
Calculate the volume of the spherical segment and the surface area of the canopy if the radius of the sphere is r=5cm and the radius of the circular base of the segment ρ=4cm. - 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?
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