# Planimetrics + cube - math problems

#### Number of problems found: 72

- 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 cm^{2}the package is larger than the surface of the cube. - Tower

Charles built a tower of cubes with an edge 2 cm long. In the lowest layer there were 6 cubes (in one row) in six rows, in each subsequent layer always 1 cube and one row less. What volume in cm^{3}did the whole tower have? - Regular square prism

The volume of a regular square prism is 192 cm^{3}. The size of its base edge and the body height is 1: 3. Calculate the surface of the prism. - Surface and volume - cube

Find the surface and volume of a cube whose wall diagonal is 5 cm long. - 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? - 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. - The funnel

The funnel has the shape of an equilateral cone. Calculate the content of the area wetted with water if you pour 3 liters of water into the funnel. - Cutting the prism

A prism with a square base with a content of 1 cm^{2}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? - 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? - Cube in sphere

The cube is inscribed in a sphere with a radius r = 6 cm. What percentage is the volume of the cube from the volume of the ball? - Angle of the body diagonals

Using vector dot product calculate the angle of the body diagonals of the cube. - Sum of the edges

The sum of the lengths of all edges of the cube is 72 cm. How many cm^{2}of colored paper are we going to use for sticking? - Inscribed circle

A circle is inscribed at the bottom wall of the cube with an edge (a = 1). What is the radius of the spherical surface that contains this circle and one of the vertex of the top cube base? - 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 - Space diagonal

The space diagonal of a cube is 129.91 mm. Find the lateral area, surface area and the volume of the cube. - Seat

How much m² of fabric do we need to sew a 50cm-shaped cube-shaped seat if 10% of the material we add to the folds? - Cube into cylinder

If we dip a wooden cube into a barrel with a 40cm radius, the water will rise 10 cm. What is the size of the cube edge? - Ribbon on the cube

A cubical gift box is tied with a piece of ribbon. If the total length of the free ends and the bow is 18 inches, what is the length of the ribbon used? (Each side of the cube is 6 inches). - Tangent spheres

A sphere with a radius of 1 m is placed in the corner of the room. What is the largest sphere size that fits into the corner behind it? Additional info: Two spheres are placed in a corner of a room. The spheres are each tangent to the walls and floor and - 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.

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Planimetrics - math problems. Cube Problems.