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