Sphere - high school - practice problems - page 3 of 5
Number of problems found: 82
- Sphere in cone
A sphere of radius 3 cm describes a cone with minimum volume. Determine cone dimensions. - 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 - 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 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?
- 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. - 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. - 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?
- 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. - Gasholder
The gasholder has a spherical shape with a diameter of 19 m. How many m³ can hold in? - 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. - 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'.
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Sphere practice problems. Examples for secondary school students.