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.

A plasticine
Jožko modeled from plasticine. He used 27g of plasticine to model a 3 cm long cube. How many grams of plasticine will it need to mold cubes with an edge of 6cm?
Length of the edge
Find the length of the edge of a cube that has a cm² surface and a volume in cm³ expressed by the same number.
Surface area of a cube
What is the surface area of a cube that has an edge of 3.5?
Cylinder
The 1.8m cylinder contains 2000 liters of water. What area (in dm²) of this container is the water?
Swimming pool
The swimming pool has the shape of a block with dimensions of 70dm, 25m, 200cm. How many hl of water can fit into the pool?
A filter
It is a pool with a volume of 3500 liters. The filter filters at 4m cubic per hour. How many minutes would it filter the entire pool?
Cube construction
A 2×2×2 cube is to be constructed using 4 white and 4 black unit cube. How many different cubes can be constructed in this way? ( Two cubes are not different if one can be obtained by rotating the other. )
Two cylinders
Two cylinders are there one with oil and one with an empty oil cylinder has no fixed value assume infinitely. We are pumping out the oil into an empty cylinder having radius =1 cm height=3 cm rate of pumping oil is 9 cubic centimeters per sec and we are p
Floating of wood - Archimedes law
What will be the volume of the floating part of a wooden (balsa) block with a density of 200 kg/m3 and a volume of 0.02 m³ that floats in alcohol? (alcohol density is 789 kg/m3)
Cheops pyramid
The Pyramid of Cheops is a pyramid with a square base with a side of 233 m and a height of 146.6 m. It made from limestone with a density of 2.7 g/cm3. Calculate the amount of stone in tons. How many trains with 30 twenty tons wagons carry the stone?
Frustum of a cone
A reservoir contains 28.54 m³ of water when completely full. The diameter of the upper base is 3.5 m while at the lower base is 2.5 m. Determine the height if the reservoir is in the form of a frustum of a right circular cone.
Barrel
Barrel of wine is filled by 9/14. What part of the barrel will remain filled when 1/4 of the wine we pour from the barrel?
Gutter pipe
How many m² of sheet metal is required to produce a 12 m long and 18 cm wide gutter, if 7% bend is required?
The cuboid
The cuboid is filled to the brim with water. The external dimensions are 95 cm, 120 cm, and 60 cm. The thickness of all walls and the bottom is 5 cm. How many liters of water fit into the cuboid?
Three glasses
Three glasses of different colors have different volumes. Red 1.5 liter is filled from 2/5, blue 3/4 liter is filled from 1/3, and the third green 1.2 liter is empty. Pour green glass 1/4 of the contents from the red glass and 2/5 of the content from the
Wood prisms
How many weight 25 prisms with dimensions 8x8x200 cm? 1 cubic meter of wood weighs 800 kg.
Rainwater
The garden area of 800 square meters fell 3mm of rainwater. How many 10 liters of water can we water this garden equally?
The glass
1 m³ of glass weighs 2600 kg. Calculate the weight of the glass glazing panel with dimensions of 2.5 m and 3.8 m if the thickness of the glass is 0.8 cm
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.
Three-quarters of its volume
The pool has a block shape with a length of 8m, a width of 5.3m and a depth of 1.5m. How many hl of water is in it if it is filled to three-quarters of its volume?

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