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.

The surface area
How much percent will the surface area of a 4x5x8 cm block increase if the length of the shortest edge is increased by 2 cm?
Surface of the cube
Find the surface of the cube that has volume 1/1m3 2/0.001 m³ 3/8000 mm³
Cuboid and ratio
Find the dimensions of a cuboid having a volume of 810 cm³ if the lengths of its edges coming from the same vertex are in ratio 2: 3: 5
Wall thickness
The hollow metal ball has an outside diameter of 40 cm. Determine the wall thickness if the weight is 25 kg and the metal density is 8.45 g/cm³.
Liquid
How much liquid does the rotary cylinder tank hold with base diameter 1.2m and height 1.5m?
Water container
The cube-shaped container is filled to two-thirds of its height. If we pour 18 liters, it will be filled to three-fifths of the height. What is the volume of the whole container?
Half-filled
A cylindrical pot with a diameter of 24 cm is half-filled with water. How many centimeters will the level rise if we add a liter of water to it?
Wax candles
A company makes wax candles in the shape of a cylinder. Each candle has a diameter of 4 inches and a height of 7 inches. If the company used 7561.12 in³ of wax, how many candles did it make? Use 3.14, and do not round your answer
Height of the cylinder
The cylinder volume is 150 dm cubic, the base diameter is 100 cm. What is the height of the cylinder?
Nádoba
Nádoba tvaru kostky je naplněna vodou do poloviny své výšky. Pokud dolijeme 20 l vody, bude nádoba naplněna do tří čtvrtin své výšky. Jaký je objem celé nádoby?
Hemisphere - roof
The shape of the observatory dome is close to the hemisphere. Its outer diameter is 11 m. How many kilograms of paint and how many liters of paint is used for its double coat if you know that 1 kg of paint diluted with 1 deciliter of paint will paint an a
Volume of the cone
Find the volume of the cone with the base radius r and the height v. a) r = 6 cm, v = 8 cm b) r = 0,9 m, v = 2,3 m c) r = 1,4 dm, v = 30 dm
Aquarium
Try to estimate the weight of the water in an aquarium 50cm long 30cm wide, when poured to a height of 25cm. Calculates the weight of the aquarium's water.
The ball
The ball has a radius of 2m. What percentage of the surface and volume is another sphere whose radius is 20% larger?
Calculate
Calculate the surface of a regular quadrilateral prism whose base edge is 2.4dm and the height of the prism is 38cm.
The prison ball
Calculate the density of the material that the prison ball is made from if you know its diameter is 15cm and its weight is approximately 2.3kg. With the help of mathematical-physicochemical tables estimate what material the ball is made from.
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?
Pool
How many hl of water is in a cuboid pool (a = 25m, b = 8m) if the area of the wetted walls is 279.2 m²?

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