Pythagorean theorem + sphere - practice problems - page 2 of 3
Number of problems found: 47
- 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. - 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. - Sphere slices
Calculate the volume and surface of a sphere if the radii of a parallel cut r1=32 cm, r2=47 cm, and its distance v=21 cm. - 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? - Stadium
A domed stadium is shaped like a spherical segment with a base radius of 150 m. The dome must contain a volume of 3500000 m³. Determine the dome's height at its center to the nearest tenth of a meter. - Cube in sphere
The cube is inscribed in a sphere with a radius r = 6 cm. What percentage is the cube's volume from the ball's volume? - Identical 35961
Nine identical spheres are stacked in the cube to fill the volume of the cube as much as possible. What part of the volume will the cube fill? - Spherical cap
Calculate the volume of the spherical cap and the areas of the spherical canopy if r = 5 cm (radius of the sphere), ρ = 4 cm (radius of the circle of the cap).
- 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? - 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? - 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. - Horizon
The top of a lighthouse is 19 m above the sea. How far away is an object just "on the horizon"? [Assume the Earth is a sphere of radius 6378.1 km.]
- Inscribed 81949
A cube is inscribed in a sphere with a radius of 27 cm. Calculate its volume and surface area. - 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. - Spherical cap
From the sphere with a radius of 11 was a truncated spherical cap. Its height is 6. What part of the volume is a spherical cap from the whole sphere? - Calculate 65354
Calculate the surface of a spherical paragraph with a height of 6 cm and a radius of 15 cm - 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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