Stereometry - examples
- Stones in aquarium
In an aquarium with a length 2 m; width 1.5 m and a depth of 2.5 m is a water level up to three-quarters of the depth. Can we place stones with a volume of 2 m3 into the aquarium without water being poured out?
The flowerbed has a length 3500mm and a width 1400mm. How many foil is needed to covers the flowerbed? How many m2 of foil was consumed for its production (add 10% of the material to the joint and waste)? How many liters of air is inside the enclosure? (F
- 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.
- 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.
Calculate the surface cube with edge 29 dm.
The swimming pool is 6 m wide and 14 m long and 185 cm deep. How many hectoliters of water is in it, if the water is 9 cm below its upper edge.
- Transforming cuboid
Cuboid with dimensions 10 cm, 9 and 17 cm is converted into a cube with the same volume. What is its edge length?
They fill shape hole with dimensions 2.5 m, 18 m, 11.8 m with 260 m3 of soil. How many percent it fill up?
Cube, which consists of 27 small cubes with edge 3 dm has volume:
From the cube of edge 52 cm was lathed maximum cylinder. What percentage of the cube is left as waste after lathed?
- Rotating cone
Calculate volume of a rotating cone with base radius r=7 cm and height h=17 cm.
- Sphere growth
How many times grow volume of sphere if radius rises 3×?
- Air mass
What is the weight of the air in a classroom with dimensions 5 m × 2 m × 3.1 m ? The air density is 1.293 kg/m3.
The cylinder-shaped container has 80 liters of water. The water reaches 45 cm height. How many liters of water will be in a container if water level extend to a height 72 cm? Write the result in liters, write down only as a whole or decimal number.
Water pipe has a cross-section 1939 cm2. An hour has passed 567 m3 of water. How much water flows through the pipe with cross-section 300 cm2 per 14 hours if water flow same speed?
- Barrel of oil
Barrel of oil weighs 282 kg. When it mold 56% oil, weighed 138 kg. What is the mass of the empty barrel?
- Volume from surface area
What is the volume of the cube whose surface area is 96 cm2?
- Fire tank
How deep is the fire tank with the dimensions of the bottom 7m and 12m, when filled with 420 m3 of water?
Into a full cylindrical tank high 2 with base radius 2.3 m we insert cuboid with dimensions 0.5 m, 1.3 m, 1.5 m. How many liters of water will come out?
- Cube wall
Surface of first cube wall his 361 cm2. Second cube area is 30% of the surface of the first cube. Determine the length of the edge of the second cube (x).