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.

Stone
When Peter threw stone in a box of water he discovered that the water level has risen by 6 cm. The box has a cuboid shape, the bottom has dimensions of 24 cm and 14 cm, height is 40 cm. What volume has a stone?
Tower model
Tower height is 300 meters, weight 8000 tons. How high is the model of the tower weight 1 kg? (State the result in the centimeters). The model is made from exactly the same material as the original no numbers need to be rounded. The result is a three-digi
Water pool
What water level is in the pool shaped cuboid with bottom dimensions of 25 m and 10 meters, when is 3750hl water in the pool.
Concrete tank
How many m³ of concrete is in the tank shape of a cuboid with dimensions of 2000 cm and 5.6 meters and 70 dm, if the concrete takes up 3/7 of the tank?
Tray
Wjat height reach water level in the tray shaped a cuboid, if it is 420 liters of water and bottom dimensions are 120 cm and 70 cm.
Juice box 2
Box with juice has the shape of a cuboid. Internal dimensions are 15 cm, 20 cm and 32 cm. If the box stay at the smallest base juice level reaches 4 cm below the upper base. How much internal volume of the box fills juice? How many cm below the top of the
Rotary cylinder 2
Base circumference of the rotary cylinder has same length as its height. What is the surface area of cylinder if its volume is 250 dm³?
Water well
Drilled well has a depth 20 meters and 0.1 meters radius. How many liters of water can fit into the well?
Copper plate
Calculate the thickness of the copper plate with a density 8.7 g/cm³ measuring 1.5 meters and 80 cm and its weight is 3.65 kg
Third dimension
Calculate the third dimension of the cuboid: a) V = 224 m³, a = 7 m, b = 4 m b) V = 216 dm³, a = 9 dm, c = 4 dm
Hectoliters
How many hectoliters of water fits into cuboid tank with dimensions of a = 3.5 m b = 2.5 m c = 1.4 m?
Reduce of the volume
Calculate how many % reduce the volume of the cube is we reduced length of each edge by 10%.
Jar
From the cylinder shaped jar after tilting spilled water so that the bottom of the jar reaches the water level accurately into half of the base. Height of jar h = 7 cm and a jar diameter D is 12 cm. How to calculate how much water remains in the jar?
Concrete box
The concrete box with walls thick 5 cm has the following external dimensions: length 1.4 m, width 38 cm and height 42 cm. How many liters of soil can fit if I fill it to the brim?
Water tank
Water tank shape of cuboid has dimensions of the bottom 7.5 meters and 3 meters. How high will reach the water in the tank will flow 10 liters of water per second and the inflow will be open 5/6 hour? (Calculate to one decimal place and the results give in
Volume of three cuboids
Calculate the total volume of all cuboids for which the the size of the edges are in a ratio of 1:2:3, and one of the edges has a size 6 cm.
Cone
Into rotating cone with dimensions r = 8 cm and h = 8 cm incribe cylinder with maximum volume so that the cylinder axis is perpendicular to the axis of the cone. Determine the dimensions of the cylinder.
Sugar cubes
The glass has 600 ml of tea, which represents 80% of the volume of the glass. If you put twenty regular sugar cubes of 2 cm in the tea, how many ml of tea are poured?
Cube 9
What was the original edge length of the cube if after cutting 39 small cubes with an edge length 2 dm left 200 dm³?
Cube volume
The cube has a surface of 384 cm². Calculate its volume.

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