Practice problems of the sphere - page 8 of 11
Number of problems found: 218
- 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? - 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. - Volume ratio
Calculate the volume ratio of balls circumscribed (diameter r) and inscribed (diameter ϱ) into an equilateral rotating cone. - 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. - Equilateral 81222
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? - 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? - One-quarter 46001
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.
- Sphere
Intersect between the plane and a sphere is a circle with a radius of 60 mm. The cone, whose base is this circle and whose apex is at the center of the sphere, has a height of 34 mm. Calculate the surface area and volume of a sphere. - 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. - 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. - Dimensions 5989
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 - 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.
- Designated 44741
Cathedral height 110m, sphere weight 6000kg, dome diameter 43m, crane arm length 25m a) what was the diameter of this sphere? b) how much mechanical work had to be done to lift it to the designated place? - 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. - Spherical 21373
The spoon has the shape of half a spherical surface with a radius of 50 mm. What volume of fluid does it fit when filled to the brim? - Float boya
A 0.5-meter spherical float is a location mark for a fishing boat anchor. It floats in salt water. Find the depth to which the float sinks if the material of which the float is made weighs 8 kilograms per cubic meter and saltwater weighs 1027 kg/m³. - 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?
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