# Pythagorean theorem + cube - math problems

#### Number of problems found: 39

• 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.
• Surface and volume - cube Find the surface and volume of a cube whose wall diagonal is 5 cm long.
• 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.
• 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.
• 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 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.
• Body diagonal Calculate the volume and surface of the cube if the body diagonal measures 10 dm.
• 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. 4 m long ladder touches the cube 1mx1m at the wall. How high reach on the wall?