# 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.

1. Water reservoir
The water tank has a cuboid with edges a= 1 m, b=2 m , c = 1 m. Calculate how many centimeters of water level falls, if we fill fifteen 12 liters cans.
2. Volume increase
How many percent will increase in the pool 50 m, width 15m if the level rises from 1m to 150cm?
3. Oak cuboid
Oak timber is rectangular shaped with dimensions of 2m, 30 cm and 15 cm. It weight is 70 kg. Calculate the weight 1 dm³ of timber.
The surface of the sphere is 60 cm square. Calculate its radius; result round to tenth of cm.
5. 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?
6. Railway wagon
The railway wagon holds 75 m3 load. Wagon can carry a maximum weight of 30 tonnes. What is the maximum density that may have material with which we could fill this whole wagon? b) what amount of peat (density 350 kg/m3) can carry 15 wagons?
7. Cubes
Carol with cut bar 12 cm x 12 cm x 135 cm to the cubes. Find the sum of all the surfaces of the resulting cubes.
8. Cube-shaped box
Design the size of the smallest possible cube-shaped box where three types of 3cm, 5cm, 6cm small cubes could be stacked to make full use of the box space (each type of cube separately). Can you find out how many smallest cubes are in the box?
9. Living room
How many people can live in a room with dimensions: a = 4m b = 5m c = 2.5m if one person needs 15m cubic space (i. E. Air . .. )?
10. Scale factor
A prism with a volume of 1458 mm3 is scaled down to a volume of 16mm3. What is the scale factor in fraction form?
11. Brick wall
Garden 70 m long and 48 m wide should surround with wall 2.1 meters high and 30 cm thick. Wall will be built on the garden ground. How many will we need bricks if to 1 m³ is required approximately 300 bricks?
12. Cube 1-2-3
Calculate the volume and surface area of the cube ABCDEFGH if: a) /AB/ = 4 cm b) perimeter of wall ABCD is 22 cm c) the sum of the lengths of all edges of the cube is 30 cm.
13. Ice and water
We want to cover rectangular rink with dimensions of 55 m and 25 m with 4cm thick layer of ice. How many liters of water we need if after freezing water increases its volume by 10%?
14. Cuboids
Two separate cuboids with different orientation in space. Determine the angle between them, knowing the direction cosine matrix for each separate cuboid. u1=(0.62955056, 0.094432584, 0.77119944) u2=(0.14484653, 0.9208101, 0.36211633)
15. Fuel economy
How many kilometers is sufficient petrol in the cylinder fuel tank with a diameter 40 cm and the base of tank length 1 m, when it is filled to 60% and if the car consume 15 liters per 100 km?
16. 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-dig
17. Cube
One cube has edge increased 5 times. How many times will larger its surface area and volume?
18. 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?
19. Cuboid - ratios
The sizes of the edges of the cuboid are in the ratio 2: 3: 5. The smallest wall have area 54 cm2. Calculate the surface area and volume of this cuboid.
20. Paper box
Hard rectangular paper has dimensions of 60 cm and 28 cm. The corners are cut off equal squares and the residue was bent to form an open box. How long must be side of the squares to be the largest volume of the box?

Do you have an interesting mathematical word problem that you can't solve it? Submit math problem, and we can try to solve it.

We will send a solution to your e-mail address. Solved examples are also published here. Please enter the e-mail correctly and check whether you don't have a full mailbox.

Please do not submit problems from current active competitions such as Mathematical Olympiad, correspondence seminars etc...