Stereometry - examples
- 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%?
Two separate cuboids with different orientation in space. Determine the angle between them, knowing the direction cosine matrix for each separate cuboid. u1=(0.62149553, 0.11709336, 0.77461762) u2=(0.046501848, 0.66652649, 0.74402958)
Calculate the surface cube with edge 25 mm.
- Transforming cuboid
Cuboid with dimensions 12 cm, 20 and 8 cm is converted into a cube with the same volume. What is its edge length?
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.
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?
From the cube of edge 52 cm was lathed maximum cylinder. What percentage of the cube is left as waste after lathed?
Cube, which consists of 27 small cubes with edge 3 dm has volume:
- 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.
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?
- 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).
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?
- Eiffel Tower
Eiffel Tower in Paris is 300 meters high, is made of steel. Its weight is 8000 tons. How tall is the tower model made of the same material, if it weigh is 4.8 kg?
The cube weighs 18 kg. How weight is cube of the same material, if its dimensions are 3-times smaller?
- Volume from surface area
What is the volume of the cube whose surface area is 96 cm2?
How high should be the milk box in the shape of a prism with base dimensions 8 cm and 14.2 cm if its volume is 1 liter?
- Fire tank
How deep is the fire tank with the dimensions of the bottom 7m and 12m, when filled with 420 m3 of water?