Sphere + expression of a variable from the formula - practice problems - page 3 of 4
Number of problems found: 72
- Cube in a sphere
The cube is inscribed in a sphere with a volume 7253 cm³. Determine the length of the edges of a cube. - Diameter 21173
The water ball has a volume of 32,500m². How big is its diameter? - 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? - 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. - 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. - 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. - 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? - Cylindrical 16713
Twenty identical steel balls were dropped into a cylindrical container of water standing on a horizontal surface to submerge them below the surface. At the same time, the water level rose by 4 mm. Determine the radius of one sphere if the diameter of the - 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. - 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'. - Above Earth
To what height must a boy be raised above the earth to see one-fifth of its surface? - 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. - Airplane
Aviator sees part of the earth's surface with an area of 200,000 square kilometers. How high does he fly? - Pilot
How high is the airplane's pilot to see 0.001 of Earth's surface? - Calculate 45991
Calculate the radius of a sphere with the same volume as a cone with a radius of 5cm and a height of 7cm. - Sphere cut
A sphere segment is cut off from a sphere k with radius r = 1. The volume of the sphere inscribed in this segment is equal to 1/6 of the segment's volume. What is the distance of the cutting plane from the center 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.
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