# Volume + diagonal - practice problems

#### Number of problems found: 58

- Side wall planes

Find the volume and surface of a cuboid whose side c is 30 cm long and the body diagonal forms angles of 24°20' and 45°30' with the planes of the side walls. - A prism

A prism with an altitude of 15cm has a base in the form of a regular octagon inscribed in a square 10cmx10cm. Find the volume of the prism. - 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. - Base diagonal

In a regular 4-sided pyramid, the side edge forms an angle of 55° with the base's diagonal. The length of the side edge is eight meters. Calculate the surface area and volume of the pyramid. - Side edges

The regular 4-sided pyramid has a body height of 2 dm, and the opposite side edges form an angle of 70°. Calculate the surface area and volume of the pyramid. - Surface and volume - cube

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

The cuboid has dimensions of 15, 20 and 40 cm. Calculate its volume and surface, the length of the body diagonal and the lengths of all three wall diagonals. - Quadrilateral prism

The height of a regular quadrilateral prism is v = 10 cm, the deviation of the body diagonal from the base is 60°. Determine the length of the base edges, the surface, and the volume of the prism. - Quadrilateral pyramid

In a regular quadrilateral pyramid, the height is 6.5 cm and the angle between the base and the side wall is 42°. Calculate the surface area and volume of the body. Round calculations to 1 decimal place. - Quadrilateral oblique prism

What is the volume of a quadrilateral oblique prism with base edges of length a = 1m, b = 1.1m, c = 1.2m, d = 0.7m, if a side edge of length h = 3.9m has a deviation from the base of 20° 35' and the edges a, b form an angle of 50.5°. - 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. - Regular hexagonal prism

Calculate the volume of a regular hexagonal prism whose body diagonals are 24cm and 25cm 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? - Block or cuboid

The wall diagonals of the block have sizes of √29cm, √34cm, √13cm. Calculate the surface and volume of the block. - Quadrilateral prism

Calculate the volume (V) and the surface (S) of a regular quadrilateral prism whose height is 28.6 cm and the deviation of the body diagonal from the base plane is 50°. - The pyramid 4s

The pyramid with a rectangular base measuring 6 dm and 8 dm has a side edge of length 13 dm. Calculate the surface area and volume of this pyramid. - Body diagonal

Calculate the volume of a cuboid whose body diagonal u is equal to 6.1 cm. Rectangular base has dimensions of 3.2 cm and 2.4 cm - Faces diagonals

If a cuboid's diagonals are x, y, and z (wall diagonals or three faces), then find the cuboid volume. Solve for x=1.3, y=1, z=1.2 - Space diagonal

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

A right pyramid on a base 4 cm square has a slanted edge of 6 cm. Calculate the volume of the pyramid.

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