# Stereometry - problems

- Cone

Circular cone with height h = 11 dm and base radius r = 4 dm slice plane parallel to the base. Calculate distance of the cone vertex from this plane, if solids have the same volume. - Cube

The sum of lengths of cube edges is 22 cm. What is its surface and volume? - Reservoir + water

Reservoir completely filled with water weighs 13 kg. After pouring off three quarters of the amount of water weights 4 kg. Calculate the weight and volume of the reservoir. - Cone and cube

About what percentage hase cone with base radius r larger volume than same high cube with square base with edge length r? - Observatory

Observatory dome has the shape of a hemisphere with a diameter d = 7 m. Calculate the surface. - Cube corners

The wooden cube with edge 45 cm was cut in 4 corners of cube with edge 5 cm. How many cubes of edge 5 cm can be even cut? - Cylinder - area

The diameter of the cylinder is one-third the length of the height of the cylinder. Calculate the surface of cylinder if its volume is 2 m^{3.} - Milk package

Milk is sold in a box with dimensions of 9.5 cm; 16.5 cm and 6.5 cm. Determine the maximum amount of milk that can fit into a box. Coating thickness is negligible. - Iron fence

One field of iron fence consists of 20 iron rods with square cross-section of 1.5 cm side and a long 1 meter. How much weight a field if the density of iron is 7800 kg/m^{3.} - Cylinder - h2

Cylinder volume is 2.7 liters. Base area is 1 dm^{2.}Calculate the height of the cylinder. - Sphere area

A cube with edge 1 m long is circumscribed sphere (vertices of the cube lies on the surface of a sphere). Determine the surface area of the sphere. - Cube and water

How many liters of water can fit into a cube with an edge length of 0.11 m? - Cuboid

The volume of the cuboid is 245 cm^{3.}Each cuboid edge length can be expressed by a integer greater than 1 cm. What is the surface area of the cuboid? - Cube edge

Determine the edges of the cube when the surface is equal to 37.5 cm square. - Cube surface area

Wall of cube has content area 95 cm square. What is the surface of the cube? - Railway wagon

The railway wagon holds 75 m^{3}load. Wagon can carry a maximum weight of 30 tonnes. What is the maximum density that may have material with which we could fill this whole wagon? b) what amount of peat (density 350 kg/m3) can carry 15 wagons? - Cube

Calculate the surface cube with edge 25 mm. - Water

Into a full cylindrical tank high 2 with base radius 2.3 m we insert cuboid with dimensions 0.5 m, 1.3 m, 1.5 m. How many liters of water will come out? - Barrel 3

Barrel with water has a weight 118 kg. When we get off 75% of water it has a weight 35 kg. How many kg has empty barrel? - Icerink

Rectangular rink with dimensions of 79.5 m and 529 dm must be covered with a layer of ice 4.5 cm thick. How many liters of water is necessary for the formation of ice when the volume of ice is 10.9% greater than the volume of water.

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