Stereometry - 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.
The sum of lengths of cube edges is 22 cm. What is its surface and volume?
- 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.
- 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.
Observatory dome has the shape of a hemisphere with a diameter d = 7 m. Calculate the surface.
- Cone and cube
About what percentage hase cone with base radius r larger volume than same high cube with square base with edge length r?
- 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.
- 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?
- Iron fence
One field of iron fence consists of 20 iron rods with square cross-section of 1.5 cm side and a long 1 meter. How much weight a field if the density of iron is 7800 kg/m3.
- 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?
- Sphere area
A cube with edge 1 m long is circumscribed sphere (vertices of the cube lies on the surface of a sphere). Determine the surface area of the sphere.
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?
- Cube edge
Determine the edges of the cube when the surface is equal to 37.5 cm square.
- 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?
- Cube surface area
Wall of cube has content area 95 cm square. What is the surface of the cube?
Calculate the surface cube with edge 29 dm.
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?
- 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.