# Cube + triangle - 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 cm3.
• 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 cm2. 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.