Solid geometry, stereometry
Solid geometry is the name for the geometry of three-dimensional Euclidean space.Stereometry involves 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.
Number of problems found: 1136
- Empty aquarium
How much does an empty aquarium weigh with dimensions: length = 40 cm, width = 30 cm, height = 20 cm, if 1 dm² of glass weighs 300 g? Calculate its weight in kilograms. - Flowerpot
The block-shaped flowerpot has external dimensions: length 1.25 m, width 10 cm, and height 11 cm. The thickness of the boards from which it is made is 0.8 cm. How many liters of soil is needed to fill it 1 cm below the top edge? What surface do we have to - Canister
Gasoline is stored in a cuboid canister having dimensions 44.5 cm, 30 cm, 16 cm. What is the total weight of a full canister when one cubic meter of gasoline weighs 710 kg and the weight of empty canister is 1.5 kg? - Children's pool
Children's pool at the swimming pool is 10m long, 5m wide and 50cm deep. Calculate: (a) how many m² of tiles are needed for lining the perimeter walls of the pool? (b) how many hectoliters of water will fit into the pool? - Runcated pyramid teapot
The 35 cm high teapot has the shape of a truncated pyramid with the length of the edge of the lower square base a=50 cm and with the edges of the rectangular base b: 20 cm and c: 30 cm. How many liters of water will fit in the teapot? - Gravel - cone
The mound of gravel has a regular circular cone shape with a height 3.3 meter and a base circumference of 18.85 meters. How many cubic meters of gravel is in a pile? Calculate the weight of gravel if its density is p = 640 kg / cubic m. - Wooden block
A cuboid-shaped wooden block has 6 cm length, 4 cm breadth, and 1 cm height. Two faces measuring 4 cm x 1 cm are colored in black. Two faces measuring 6 cm x 1 cm are colored in red. Two faces measuring 6 cm x 4 cm are colored in green. The block is divid - Water reservoir
The cuboid reservoir contains 1900 hectoliters of water and the water height is 2.5 m. Determine the dimensions of the bottom where one dimension is 3.2 m longer than the second one. - The pool
The pool is 25 meters long, 10 meters wide and 1.5 meters deep. How many liters are needed to fill it completely? How much will the new floor and wall paneling cost if one m² costs 10 euros? - Rainfall
The annual average rainfall in India was in Cherrapunji in the year 1981 26 461 mm. How many hectoliters of water fell on 1 m²? Would fit this amount of water into a cube of three meters? - Juice box 2
Box with juice has the shape of a cuboid. Internal dimensions are 15 cm, 20 cm, and 32 cm. Suppose the box stays 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 bas - How much
How much money will we pay for 20 planks 4m long, 15cm wide and 26mm thick when 1m³ of wood costs 4500kč? - Cube
The sum of all cube edges is 30cm. Find the surface area of the cube. - Three dice
When you throw three dice was the sum total of the dice 10. The yellow dice fell one eye more than on the red and brown fell 3 eyes less than red. How many eyes fell on every dice? - 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 thinner is used for its double coat if you know that 1 kg of paint diluted with 1 deciliter of thinner will paint - Aquarium
Find how many dm² of glass we need to make a block-shaped aquarium (the top is not covered) if the dimensions of the aquarium are to be: width 50 cm, length 120 cm, and height 8.5 dm. - 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 - Concrete box
The concrete box with walls thick 7 cm has the following external dimensions: length 1.8 m, width 44 cm and height 46 cm. How many liters of soil can fit if I fill it to the brim? - Roof repair
To repair the roof, we need 15 pieces of boards 6 m long, 15 cm wide and 25 mm thick. How many euros will we pay for all boards if 1 m³ of boards costs 500 euros? - Oak trunk
Calculate in tonnes the approximate weight of a cylindrical oak trunk with a diameter of 66 cm and a length of 4 m, knowing that the density of the wood was 800 kg/m³.
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