Sphere - practice for 14 year olds - page 4 of 6
Number of problems found: 115
- 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 - 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? - 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? - Two balls
Two balls, one 8 cm in radius and the other 6 cm in radius, are placed in a cylindrical plastic container 10 cm in radius. Find the volume of water necessary to cover them. - Sphere vs cube
How much % of the surface of a sphere of radius 12 cm is the surface of a cube inscribed in this sphere? - Inscribed cube
A cube is inscribed in a sphere with a radius of 27 cm. Calculate its volume and surface area. - Chemical parison
The blown parison (with the shape of a sphere) has a volume of 1.9 liters. What is its surface? - 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 - Cube in sphere
The sphere is an inscribed cube with an edge of 8 cm. Find the sphere's radius. - 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? - Cost of Granite Pedestals
The owners of the ornamental garden decided to beautify the entrance to the garden with two granite plinths composed of a prism and a sphere. The sphere has a diameter of 56 cm; the prism has dimensions of 60 cm, 60 cm, and 150 cm. How much will the owner - Vertex angle - cone
The rotating cone has a height of 72 cm and an angle at the top of 72°. Determine the volume of a sphere with the same radius as the cone. - Sphere surface
Express in square centimeters the surface of a sphere whose radius is equal to one-quarter of the radius of the cone. The diameter of the base of the cone is 20 cm. - 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? - 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. - MO SK/CZ Z9–I–3
John had a ball that rolled into a pool and floated on the water. Its highest point was 2 cm above the surface. The diameter of the circle where the ball met the water surface was 8 cm. Find the diameter of John's ball. - Float boya
A spherical float with a diameter of 0.5 m marks the location of a fishing boat's anchor. It floats in salt water. Find the depth to which the float sinks if the material it is made of has a density of 8 kg/m³ and salt water has a density of 1,027 kg/m³. - 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. - Big Earth
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. - 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.
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