# Solid geometry, stereometry - page 15

Solid geometry is the name for the geometry of three-dimensional Euclidean space.Stereometry deals with the measurements of volumes of various solid figures (three-dimensional figures) including pyramids, prisms and other polyhedrons; cylinders; cones; truncated cones; and balls bounded by spheres.

- Cuboid - Vab

Find the surface of the cuboid when its volume is 52.8 cubic centimeters, and the length of its two edges is 2 centimeters and 6 centimeters. - Cube, cuboid, and sphere

Volumes of a cube and a cuboid are in ratio 3: 2. Volumes of sphere and cuboid are in ratio 1: 3. In what ratio are the volumes of cube, cuboid, and sphere? - Equilateral cylinder

A sphere is inserted into the rotating equilateral cylinder (touching the bases and the shell). Prove that the cylinder has both a volume and a surface half larger than an inscribed sphere. - Volume and body diagonal

Calculate how much the volume and body diagonal of the cuboid decrease if we reduce each of its three edges a, b, c by 18%? - The tank

The tank is full up to 4/5 of the total height and contains 240 hl of water. The area of the base is 6 square meters. What is the height of the tank? - Cube into sphere

The cube has brushed a sphere as large as possible. Determine how much percent was the waste. - Circular pool

The 3.6-meter pool has a depth of 90 cm. How many liters of water is in the pool? - Big cube

Calculate the surface of the cube, which is composed of 64 small cubes with an edge 1 cm long. - How much

How much money will we pay for 20 planks 4m long, 15cm wide and 26mm thick when 1m³ of wood costs 4500kč? - Water tank

A 288 hectoliter of water was poured into the tank with dimensions 12 m and 6 m bottom and 2 m depth. What part of the volume of the tank water occupied? Calculate the surface of tank wetted with water. - Cube edges

The sum of the lengths of the cube edges is 42 cm. Calculate the surface of the cube. - Cylindrical container

An open-topped cylindrical container has a volume of V = 3140 cm^{3.}Find the cylinder dimensions (radius of base r, height v) so that the least material is needed to form the container. - Cuboid

The sum of the lengths of the three edges of the cuboid that originate from one vertex is 210 cm. Edge length ratio is 7: 5: 3. Calculate the length of the edges. - Rainfall

A rectangular garden of 25m in length and width 20m in width fall 4mm of water. Express by a fraction in basic form what part of the 60-hectolitre tank we would fill with this water. - Cube edges

If the edge length of the cube increases by 50%, how does the volume of this cube increase? - Basen

How many square meters of tiles we need to tile the walls and floor of the pool 15 meters long, six meters wide and two meters?deep - Rain

It rains at night. On 1 m^{2}of lake will drop 60 liters of water. How many cm will the lake level rise? - Inscribed

Cube is inscribed in the cube. Determine its volume if the edge of the cube is 10 cm long. - Cylinder-shaped vase

If the cylinder-shaped vase is filled with water up to 35 cm, it contains 1 liter of water. How much water will it contain if it is filled to a height of 45cm? - Hectoliters

How many hectoliters of water is in garden barrel with 90 cm diameter and a height of 1.3 m, if it is filled to 80% of its capacity?

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