# Right triangle + cube - math problems

#### Number of problems found: 34

- Surface and volume - cube

Find the surface and volume of a cube whose wall diagonal is 5 cm long. - 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. - Angle of the body diagonals

Using vector dot product calculate the angle of the body diagonals of the cube. - 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? - Space diagonal

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

Calculate the length of the side and the diagonals of the cube with a volume of 27 cm^{3}. - Body diagonal

Calculate the cube volume, whose body diagonal size is 75 dm. Draw a picture and highlight the body diagonal. - Cube diagonals

The cube has a wall area of 81 cm square. Calculate the length of its edge, wall, and body diagonal. - 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 cm^{2}. Find the area of the - Cube cut

The cube ABCDA'B'C'D ' has an edge of 12cm. Calculate the area of diagonal cut B DD'B '. - Body diagonal - cube

Calculate the surface and cube volume with body diagonal 15 cm long. - Body diagonal

Calculate the length of the body diagonal of the 6cm cube. - Calculate

Calculate the length of the wall diagonal of the cube with an edge 5 cm long. - Cube wall

The perimeter of one cube wall is 120 meters. Calculate the surface area and the body diagonal of this cube. - Cube wall

Calculate the cube's diagonal if you know that one wall's surface is equal to 36 centimeters square. Please also calculate its volume. - Cube in sphere

The sphere is an inscribed cube with an edge of 8 cm. Find the sphere's radius. - Ladder

4 m long ladder touches the cube 1mx1m at the wall. How high reach on the wall? - Cube and sphere

Cube with the surface area 150 cm^{2}is described sphere. What is sphere surface?

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