Solid geometry, stereometry

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.

Pebble
The aquarium with internal dimensions of the bottom 40 cm × 35 cm and a height of 30 cm is filled with two-thirds of water. Calculate how many millimeters the water level in the aquarium rises by dipping a pebble-shaped sphere with a diameter of 18 cm.
TV transmitter
The volume of water in the rectangular swimming pool is 6998.4 hectoliters. The promotional leaflet states that if we wanted all the pool water to flow into a regular quadrangle with a base edge equal to the average depth of the pool, the prism would have.
Rectangular cuboid
The rectangular cuboid has a surface area 5334 cm², its dimensions are in the ratio 2:4:5. Find the volume of this rectangular cuboid.
Pool
The swimming pool is 10 m wide and 8 m long and 153 cm deep. How many hectoliters of water is in it, if the water is 30 cm below its upper edge?
Transforming cuboid
Cuboid with dimensions 6 cm, 10, and 11 cm is converted into a cube with the same volume. What is its edge length?
Sphere
The surface of the sphere is 12100 cm², and weight is 136 kg. What is its density?
Pipes
Water pipe has a cross-section 1087 cm². An hour has passed 960 m³ of water. How much water flows through the pipe with cross-section 300 cm² per 9 hours if water flow same speed?
Eiffel Tower
Eiffel Tower in Paris is 300 meters high, is made of steel. Its weight is 8000 tons. How tall is the tower model made of the same material, if it weigh is 2.4 kg?
Tanks
Fire tank has cuboid shape with a rectangular floor measuring 13.7 m × 9.8 m. Water depth is 2.4 m. Water was pumped from the tank into barrels with a capacity of 2.7 hl. How many barrels were used, if the water level in the tank fallen 5 cm? Wr
Gutter
How much metal is needed for production 46 pieces of gutter pipes with the diameter 12 cm and length of 4 m? The plate bends add 2% of the material.
Barrel of oil
Barrel of oil weighs 283 kg. When it mold 26% oil, weighed 216 kg. What is the mass of the empty barrel?
Cube zoom
How many percent we increase volume and surface of cube, if we magnify its edge by 38%.
Bricks
Brick has volume 2.2 dm³. How many bricks can drive truck with capacity 23 ton? The density of brick is 1.6 g/cm³.
Sandpile
Auto sprinkled with sand to an approximately conical shape. Workers wanted to determine the volume (amount of sand) and therefore measure the circumference of the base and the length of both sides of the cone (over the top). What is the volume of the san
Lathe
From the cube of edge 37 cm was lathed maximum cylinder. What percentage of the cube is left as waste after lathed?
Rotation
The right triangle with legs 14 cm and 20 cm rotate around the longer leg. Calculate the volume and surface area of the formed cone.
Air mass
What is the weight of the air in a classroom with dimensions 10 m × 10 m × 2.7 m ? The air density is 1.293 kg/m³.
Cube
Calculate the surface cube with edge 11 dm.
Prism X
The prism with the edges of the lengths x cm, 2x cm and 3x cm has volume 20250 cm³. What is the area of surface of the prism?
Hollow sphere
Calculate the weight of a hollow tungsten sphere (density 19.3 g/cm³), if the inner diameter is 14 cm and wall thickness is 3 mm.

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