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: 1064

Solid in water
The solid weighs in air 19.9 g and in water 17 g. Calculate the density of the solid.
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).
Ladder
4 m long ladder touches the cube 1mx1m at the wall. How high reach on the wall?
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?
Vector
Calculate length of the vector v⃗ = (9.75, 6.75, -6.5, -3.75, 2).
Angle of the body diagonals
Using vector dot product calculate the angle of the body diagonals of the cube.
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)
Forces
In point O acts three orthogonal forces: F₁ = 20 N, F₂ = 7 N, and F₃ = 19 N. Determine the resultant of F and the angles between F and forces F₁, F₂, and F₃.
Solid cuboid
A solid cuboid has a volume of 40 cm³. 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.
Airplane
Aviator sees part of the earth's surface with an area of 200,000 square kilometers. How high he flies?
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?
Distance of lines
Find the distance of lines AE, CG in cuboid ABCDEFGH, if given | AB | = 3cm, | AD | = 2 cm, | AE | = 4cm
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 cm³ 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
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.
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.
Right circular cone
The volume of a right circular cone is 5 liters. Calculate the volume of the two parts into which the cone is divided by a plane parallel to the base, one-third of the way down from the vertex to the base.
The truncated
The truncated rotating cone has bases with radii r1 = 8 cm, r2 = 4 cm and height v = 5 cm. What is the volume of the cone from which the truncated cone originated?
Cutting cone
A cone with a base radius of 10 cm and a height of 12 cm is given. At what height above the base should we divide it by a section parallel to the base so that the volumes of the two resulting bodies are the same? Express the result in cm.
Secret treasure
Scouts have a tent in the shape of a regular quadrilateral pyramid with a side of the base 4 m and a height of 3 m. Find the container's radius r (and height h) so that they can hide the largest possible treasure.

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