Body volume - problems
Circular cone with height h = 11 dm and base radius r = 4 dm slice plane parallel to the base. Calculate distance of the cone vertex from this plane, if solids have the same volume.
- Floating barrel
Barrel (cylinder shape) floats on water, top of barrel is 7 dm above water and the width of surfaced barrel part is 20 dm. Barrel length is 27 dm. Calculate the volume of the barrel.
- Reservoir + water
Reservoir completely filled with water weighs 13 kg. After pouring off three quarters of the amount of water weights 4 kg. Calculate the weight and volume of the reservoir.
- Tetrahedral prism
Calculate surface and volume tetrahedral prism, which has a rhomboid-shaped base, and its dimensions are: a = 12 cm, b = 7 cm, ha = 6 cm and prism height h = 10 cm.
- Hexagonal pyramid
Calculate the volume and the surface of a regular hexagonal pyramid with a base edge length 3 cm and a height 5 cm.
- Cube corners
The wooden cube with edge 45 cm was cut in 4 corners of cube with edge 5 cm. How many cubes of edge 5 cm can be even cut?
- Cylinder - area
The diameter of the cylinder is one-third the length of the height of the cylinder. Calculate the surface of cylinder if its volume is 2 m3.
- Milk package
Milk is sold in a box with dimensions of 9.5 cm; 16.5 cm and 6.5 cm. Determine the maximum amount of milk that can fit into a box. Coating thickness is negligible.
- Cylinder - h2
Cylinder volume is 2.7 liters. Base area is 1 dm2. Calculate the height of the cylinder.
- Cube and water
How many liters of water can fit into a cube with an edge length of 0.11 m?
The volume of the cuboid is 245 cm3. Each cuboid edge length can be expressed by a integer greater than 1 cm. What is the surface area of the cuboid?
- Prism - box
The base of prism is a rectangle with a side of 7.5 cm and 12.5 cm diagonal. The volume of the prism is V = 0.9 dm3. Calculate the surface of the prism.
- Hexa prism
Determine the volume of hex prism with edge base 4 cm. The body height is 28 cm.
Calculate the height of the prism having a surface area 448.88 dm² wherein the base is square with a side of 6.2 dm. What will be its volume in hectoliters?
- 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?
Calculate volume of pillar shape of a regular tetrahedral truncated pyramid, if his square have sides a = 17, b = 22 and height is v = 36.
- Barrel 3
Barrel with water has a weight 118 kg. When we get off 75% of water it has a weight 35 kg. How many kg has empty barrel?
Rectangular rink with dimensions of 79.5 m and 529 dm must be covered with a layer of ice 4.5 cm thick. How many liters of water is necessary for the formation of ice when the volume of ice is 10.9% greater than the volume of water.
- Weight of air
What is the weight of air in the living room measuring width 8 m length 2 m and height 2.7 m? Air density is ρ = 1.2 kg/m3.
Calculate height and volume of a regular tetrahedron whose edge has a length 11 cm.