Sphere + triangle - practice problems
Number of problems found: 46
- The spacecraft
The spacecraft spotted a radar device at an altitude angle alpha = 34 degrees 37 minutes and had a distance of u = 615km from Earth's observation point. Calculate the distance d of the spacecraft from Earth at the moment of observation. Earth is considere - Sphere from tree points
Equation of sphere with three-point (a,0,0), (0, a,0), (0,0, a) and center lies on plane x+y+z=a - Moon
We see the Moon from the perspective angle 28'. At the time of the full Moon, the Moon's radius is 1740 km. Calculate the mean distance of the Moon from the Earth. - Rotation of the Earth
Calculate the circumferential speed of the Earth's surface at a latitude of 34.5°. Consider a globe with a radius of 6378 km.
- Sphere cuts
At what distance from the center does the sphere intersect with the radius R = 46 plane if the cut area and area of the main sphere circle are in ratio 2/5? - 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.] - Sphere equation
Obtain the equation of a sphere. Its center is on the line 3x+2z=0=4x-5y and passes through the points (0,-2,-4) and (2,-1,1). - Earth parallel
Earth's radius is 6377 km long. Calculate the length parallel to latitude 75°. - Earth's circumference
Calculate the Earth's circumference of the parallel 48 degrees and 10 minutes.
- Cubes
One cube is an inscribed sphere, and the other one is described. Calculate the difference of volumes of cubes if the difference of surfaces in 231 cm². - Billiard balls
A layer of ivory billiard balls radius of 6.35 cm is in the form of a square. The balls are arranged so that each ball is tangent to everyone adjacent to it. In the spaces between sets of 4 adjacent balls, other balls rest, equal in size to the original. - 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 the corner of a room. The spheres are each tangent to the walls and floor an - 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. - Identical 35961
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?
- 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? - Sphere in cone
A sphere is inscribed in the cone (the intersection of their boundaries consists of a circle and one point). The ratio of the ball's surface and the area of the base is 4:3. A plane passing through the axis of a cone cuts the cone in an isosceles triangle - Confectionery 7318
The confectioner needs to carve a cone-shaped decoration from a ball-shaped confectionery mass with a radius of 25 cm. Find the radius of the base of the ornament a (and the height h). He uses as much material as possible is used to make the ornament. - Cube and sphere
A cube with a surface area of 150 cm² is described sphere. What is a sphere surface? - Cube in sphere
The sphere is an inscribed cube with an edge of 8 cm. Find the sphere's radius.
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?Do you have homework that you need help solving? Ask a question, and we will try to solve it. Solving math problems.
