# Solid geometry + area - practice problems

#### Number of problems found: 588

- 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. - Decagon prism

A regular decagon of side a = 2 cm is the base of the perpendicular prism, the side walls are squares. Find the prism volume in cm^{3}, round to two decimal places. - Equilateral cylinder

A sphere is inserted into the rotating equilateral cylinder (touching the bases and the shell). Prove that the cylinder has both a volume and a surface half larger than an inscribed sphere. - 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. - Four sided prism

Calculate the volume and surface area of a regular quadrangular prism whose height is 28.6cm and the body diagonal forms a 50-degree angle with the base plane. - Cone

Calculate volume and surface area of the cone with a diameter of the base d=15 cm and side of the cone with the base has angle 52°. - 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 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°. - Tetrahedral pyramid

Determine the surface of a regular tetrahedral pyramid when its volume is V = 120 and the angle of the sidewall with the base plane is α = 42° 30'. - 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. - 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°. - Prism diagonal

The body diagonal of a regular square prism has an angle of 60 degrees with the base, the edge length is 10 cm. What is the volume of the prism? - Pilot

How high is the airplane's pilot to see 0.001 of Earth's surface? - Angle of deviation

The surface of the rotating cone is 30 cm² (with circle base), its surface area is 20 cm². Calculate the deviation of the side of this cone from the plane of the base. - Octagonal pyramid

Find the volume of a regular octagonal pyramid with height v = 100 and the angle of the side edge with the plane of the base is α = 60°. - Pyramid 8

Calculate the volume and the surface area of a regular quadrangular pyramid with the base side 9 cm and side wall with the base has an angle 75°. - Glass

How many glass are needed to produce glass with base regular 5-gon if one base triangle in the base is 4.2 square cm and the height is 10 cm? - Pentagonal prism

The regular pentagonal prism is 10 cm high. The radius of the circle of the described base is 8 cm. Calculate the volume and surface area of the prism. - Rotary cone

The volume of the rotation of the cone is 472 cm^{3}, and the angle between the side of the cone and the base angle is 70°. Calculate the lateral surface area of this cone. - The roof

The roof of the tower has the shape of a regular quadrangular pyramid, the base edge of which is 11 m long and the side wall of the animal with the base an angle of 57°. Calculate how much roofing we need to cover the entire roof, if we count on 15% waste

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Solid geometry, stereometry. Area - math word problems.