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.

The cube
The cube has an edge of 25 cm. We cut it into small cubes of 5 cm long side. How many of these little ones left when we build a new cube of 20 cm in length?
Bottle
A company wants to produce a bottle whose capacity is 1.25 liters. Find the dimensions of a cylinder that will be required to produce this 1.25litres if the hight of the cylinder must be 5 times the radius.
Perfect cubes
Suppose a number is chosen at random from the set (0,1,2,3,. .. ,202). What is the probability that the number is a perfect cube?
A residential
A residential colony has a population of 5400 and 60 litres of water is required per person per day. For the effective utilization of rain water, they constructed a water reservoir measuring 48m × 27m × 25m to collect the rain water. For how many days, the
The volume
The volume of a solid cylinder is 260 cm³ the cylinder is melt down into a cuboid, whose base is a square of 5cm, calculate the height of the cuboid and the surface area of the cuboid
Cube walls
Find the volume and the surface area of the cube if the area of one of its walls is 40 cm².
The number
The number of 1 cm cubes required to make 4 cm cube is?
Cylinder melted into cuboid
A circular cylinder has area of cross section 56cm² and the height is 10cm the cylinder is melted and made into a cuboid of base area 16cm². What is the height of the cuboid?
Water tank
What is the height of the cuboid-shaped tank with the bottom dimensions of 80 cm and 50 cm if the 480 liters of water reaches 10 cm below the top?
Sphere floating
Will float a hollow iron ball with an outer diameter d1 = 20cm and an inside diameter d2 = 19cm in the water? The iron density is 7.8 g/cm 3. (Instructions: Calculate the average sphere density and compare with the density of the water. )
Dort
The cube-shaped cube box has the dimensions of 30 cm × 30 cm × 12 cm. How many CZK (Czech crowns) would cost be the biggest cake that would fit into the box when a 10 cm³ cake costs CZK 0.5? The cake has the same shape as the box.
The cube
The cube has an edge of 12 dm. The second cube has an edge exactly 20% longer. How many % is more water in the second cube than in the first cube, if the first cube is full to 3/4 and the second to 3/8?
Sphere VS
Find the surface and volume of a sphere that has a radius of 2 dm.
Sphere radius
The radius of the sphere we reduce by 1/3 of the original radius. How much percent does the volume and surface of the sphere change?
Half-sphere roof
The roof above the castle tower has the shape of a 12.8 m diameter half-sphere. What is the cost of this roof, if the cost of 1 square meter is 12 euros and 40 cents?
Area to volume
If the surface area of a cube is 486, find its volume.
A cylindrical tank
A cylindrical tank can hold 44 cubic meters of water. If the radius of the tank is 3.5 meters, how high is the tank?
Bucket
The bucket half filled with water weighs 5.55 kg, the full bucket weighs 9.85 kg. How much does the bucket weigh?
No smoke
Tobacco company NO-SMOKE adorned its stand at the cigarette-type trade fair with the cigarette-shaped. The dimensions of which were 20 times the size of a regular cigarette. The regular cigarette contains 0.8 mg of nicotine. How much nicotine would a giant
Volume of ball
Find the volume of a volleyball that has a radius of 4 1/2 decimeters. Use 22/7 for π

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