Practice problems of the cube

Number of problems found: 260

Cube wall
The surface of the first cube wall is 64 m². The second cube area is 40% of the surface of the first cube. Determine the length of the edge of the second cube (x).
Cube in ball
Cube is inscribed into the sphere of radius 181 dm. How many percent is the volume of cube of the volume of the sphere?
Plasticine ball
Plasticine balls have radius r₁=85 cm, r₂=60 mm, r₃=59 cm, r₄=86 cm, r₅=20 cm, r₆=76 mm, r₇=81 mm, r₈=25 mm, r₉=19 mm, r₁₀=14 cm. For these balls
Eiffel Tower
Eiffel Tower in Paris is 300 meters high and is made of steel. Its weight is 8000 tons. How tall is the tower model made of the same material if it weighs is 2.4 kg?
Endless lego set
The endless lego set contains only 6, 9, 20 kilograms blocks that can no longer be polished or broken. The workers took them to the gym and immediately started building different buildings. And of course, they wrote down how much the building weighed. The
Chocolate roll
The cube of 5 cm chocolate roll weighs 30 g. How many calories will contain the same chocolate roller of a prism shape with a length of 0.5 m whose cross-section is an isosceles trapezoid with bases 25 and 13 cm and legs 10 cm? You know that 100 g of this
Pyramid cut
We cut the regular square pyramid with a parallel plane to the two parts (see figure). The volume of the smaller pyramid is 20% of the volume of the original one. The bottom of the base of the smaller pyramid has a content of 10 cm². Find the area of the
The pool
The cube-shaped pool has 140 cubic meters of water. Determine the dimensions of the bottom if the depth of the water is 200 cm and one dimension of the base is 3 m greater than the other. What are the dimensions of the pool bottom?
Bricks pyramid
How many 50cm x 32cm x 30cm brick needed to built a 272m x 272m x 278m pyramid?
Cube cut
In the ABCDA'B'C'D'cube, it is guided by the edge of the CC' a plane witch dividing the cube into two perpendicular four-sided and triangular prisms, whose volumes are 3:2. Determine in which ratio the edge AB is divided by this plane.
The height of prism
The base of the perpendicular prism is formed by a right triangle with perpendiculars 30 cm and 40 cm long. This prism has the same volume as a cube with an edge length of 3 dm. Find its height in cm.
Regular square prism
The volume of a regular square prism is 192 cm³. The size of its base edge and the body height is 1: 3. Calculate the surface of the prism.
Wallpaper
3750 cm square of wallpaper is needed to glue a cube-shaped box. Can Dad cut out the whole necessary piece of wallpaper as a whole if he has a roll of wallpaper 50 cm wide?
Alien ship
The alien ship has the shape of a sphere with a radius of r = 3000m, and its crew needs the ship to carry the collected research material in a cuboid box with a square base. Determine the length of the base and (and height h) so that the box has the large
Body diagonal
The cuboid has a volume of 32 cm³. Its side surface area is double as one of the square bases. What is the length of the body diagonal?
A butter
A butter cube with an edge 6.5 cm long is packed in a package with dimensions a = 28 cm, b = 15 cm. Calculate how many cm² the package is larger than the surface of the cube.
Truncated cone 6
Calculate the volume of the truncated cone whose bases consist of an inscribed circle and a circle circumscribed to the opposite sides of the cube with the edge length a=1.
Rectangle pool
Find dimensions of an open pool with a square bottom with a capacity of 32 m³ to have painted/bricked walls with the least amount of material.
Pyramid in cube
In a cube with an edge 12 dm long, we have an inscribed pyramid with the apex at the center of the cube's upper wall. Calculate the volume and surface area of the pyramid.
Cutting the prism
A prism with a square base with a content of 1 cm² and a height of 3 cm was cut from a cube with an edge length of 3 cm. What is the surface of the body formed from the cube after cutting the prism?

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