# Solid geometry, stereometry

Solid geometry is the name for the geometry of three-dimensional Euclidean space.Stereometry deals with the measurements of volumes of various solid figures (three-dimensional figures) including pyramids, prisms and other polyhedrons; cylinders; cones; truncated cones; and balls bounded by spheres.

#### Number of problems found: 1005

- Solid in water

The solid weighs in air 19.9 g and in water 17 g. Calculate the density of the solid. - Ladder

4 m long ladder touches the cube 1mx1m at the wall. How high reach on the wall? - Angle of the body diagonals

Using vector dot product calculate the angle of the body diagonals of the cube. - Cone

If the segment of the line y = -3x +4 that lies in quadrant I is rotated about the y-axis, a cone is formed. What is the volume of the cone? - Airplane

Aviator sees part of the earth's surface with an area of 200,000 square kilometers. How high he flies? - Vector

Calculate length of the vector v⃗ = (9.75, 6.75, -6.5, -3.75, 2). - Sphere equation

Obtain the equation of sphere its centre on the line 3x+2z=0=4x-5y and passes through the points (0,-2,-4) and (2,-1,1). - Forces

In point O acts three orthogonal forces: F_{1}= 20 N, F_{2}= 7 N, and F_{3}= 19 N. Determine the resultant of F and the angles between F and forces F_{1}, F_{2}, and F_{3}. - A square base

A solid right pyramid has a square base. The length of the base edge is 4 centimeters and the height of the pyramid is 3 centimeters. What is the volume of the pyramid? - Solid cuboid

A solid cuboid has a volume of 40 cm^{3}. The cuboid has a total surface area of 100 cm squared. One edge of the cuboid has a length of 2 cm. Find the length of a diagonal of the cuboid. Give your answer correct to 3 sig. Fig. - Cuboids

Two separate cuboids with different orientation in space. Determine the angle between them, knowing the direction cosine matrix for each separate cuboid. u1=(0.62955056, 0.094432584, 0.77119944) u2=(0.14484653, 0.9208101, 0.36211633) - Angle of two lines

There is a regular quadrangular pyramid ABCDV; | AB | = 4 cm; height v = 6 cm. Determine the angles of lines AD and BV. - The volume

The volume of a solid cylinder is 260 cm^{3}the cylinder is melt down into a cuboid, whose base is a square of 5cm, calculate the height of the cuboid and the surface area of the cuboid - Distance of lines

Find the distance of lines AE, CG in cuboid ABCDEFGH, if given | AB | = 3cm, | AD | = 2 cm, | AE | = 4cm - Brick wall

What is the weight of a solid brick wall that is 30 cm wide, 4 m long and 2 m high? The density of the brick is 1500 kg per cubic meter. - The cube - simple

Calculate the surface of the cube measuring 15 centimeters. - Observatory

Observatory dome has the shape of a hemisphere with a diameter d = 20 m. Calculate the surface. - Distance of points

A regular quadrilateral pyramid ABCDV is given, in which edge AB = a = 4 cm and height v = 8 cm. Let S be the center of the CV. Find the distance of points A and S. - Ratio

The radii of two cones are in the ratio 5.7 Calculate the area ratio if cones have same height. - Hectoliter into cube

Can 1hl of water fit into a half-meter cube?

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