Sphere - practice for 13 year olds - page 5 of 6
Number of problems found: 117
- Balls
Three metal balls with volumes V1=81 cm³ V2=96 cm³ and V3=28 cm³ melted into one ball. Determine its surface area. - 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. - 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. - Diameter 21173
The water ball has a volume of 32,500m². How big is its diameter?
- Inscribed 81949
A cube is inscribed in a sphere with a radius of 27 cm. Calculate its volume and surface area. - 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 - 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? - 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. - 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 - 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? - 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?
- Hemisphere-shaped 7829
The ice cream maker sold 6l of ice cream a day. How many hemisphere-shaped portions with a diameter of 6 cm could he make from the ice cream sold? - 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. - 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. - Half-sphere roof
The roof above the castle tower has the shape of a 12.8 m diameter half-sphere. What is this roof's cost if the cost of 1 square meter is 12 euros and 40 cents? - A sphere
A sphere has a radius of 5.5 cm. Determine its volume and surface area. A frustum of the sphere is formed by two parallel planes. One through the diameter of the curved surface of the frustum is to be of the surface area of the sphere. Find the height and
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