# Volume + Pythagorean theorem - math problems

#### Number of problems found: 152

• The volume The volume of the cone is 94.2dm³, the radius of the base is 6 dm Calculate the surface of the cone.
• Surface and volume Find the surface and volume of the rotating cone if the circumference of its base is 62.8 m and the side is 25 m long.
• 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?
• Surface and volume - cube Find the surface and volume of a cube whose wall diagonal is 5 cm long.
• Tetrahedron Calculate height and volume of a regular tetrahedron whose edge has a length 6 cm.
• Volume of the cone Calculate the volume of the cone if the content of its base is 78.5 cm2 and the content of the shell is 219.8 cm2.
• Cube diagonals Calculate the length of the side and the diagonals of the cube with a volume of 27 cm3.
• Cone - from volume surface area The volume of the rotating cone is 1,018.87 dm3, and its height is 120 cm. What is the surface area of the cone?
• Maximum of volume The shell of the cone is formed by winding a circular section with a radius of 1. For what central angle of a given circular section will the volume of the resulting cone be maximum?
• Triangular pyramid What is the volume of a regular triangular pyramid with a side 3 cm long?
• Cone Calculate the volume of the rotating cone with a base radius 26.3 cm and a side 38.4 cm long.
• Hexagonal pyramid The base of the pyramid is a regular hexagon, which can be circumscribed in a circle with a radius of 1 meter. Calculate the volume of a pyramid 2.5 meters high.
• Pyramid a+h Calculate the pyramid's volume and surface area with the edge and height a = 26 cm. h = 3 dm.
• Axial section Calculate the volume and surface of a cone whose axial section is an equilateral triangle with side length a = 18cm.
• Body diagonal Calculate the volume and surface of the cube if the body diagonal measures 10 dm.
• Cuboid - volume, diagonals The length of the one base edge of cuboid a is 3 cm. Body diagonal is ut=13 cm and diagonal of cuboid's baseis u1=5 cm. What is the volume of the cuboid?
• Pyramid height Find the volume of a regular triangular pyramid with edge length a = 12cm and pyramid height h = 20cm.
• 3s prism It is given a regular perpendicular triangular prism with a height of 19.0 cm and a base edge of 7.1 cm. Calculate the volume of the prism.
• Tetrahedral pyramid Calculate the surface S and the volume V of a regular tetrahedral pyramid with the base side a = 5 m and a body height of 14 m.
• Frustrum - volume, area Calculate the surface and volume of the truncated cone, the radius of the smaller figure is 4 cm, the height of the cone is 4 cm and the side of the truncated cone is 5 cm.

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