Solid geometry, stereometry - last pageSolid geometry is the name for the geometry of three-dimensional Euclidean space.
Stereometry involves 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: 2099
- Calculate 32281
The rotating cone has a base radius r = 226mm, and the deviation of the side from the base plane is 56 °. Calculate the height of the cone.
- Heptagonal pyramid
A hardwood for a column is in the form of a frustum of a regular heptagonal pyramid. The lower base edge is 18 cm, and the upper base of 14 cm. The altitude is 30 cm. Determine the weight in kg if the wood density is 10 grams/cm³.
- Sphere in cone
A sphere is inscribed in the cone (the intersection of their boundaries consists of a circle and one point). The ratio of the ball's surface and the area of the base is 4:3. A plane passing through the axis of a cone cuts the cone in an isosceles triangle
Calculate the angle between box base 9 x 14 and body diagonal length 18.
- Cube - angles
Calculate the angle between the wall diagonal and cube base. Calculate the angle between the cube body diagonal and the cube base.
- ----------------- 4850
v = 35 m α = 55 ° β = 15 ° ----------------- X =? Calculate: V- barrack volume =? S- barrack area =?
- What percentage
What percentage of the Earth's surface is seen by an astronaut from a height of h = 350 km? Take the Earth as a sphere with a radius R = 6370 km.
- Earth's circumference
Calculate the Earth's circumference of the parallel 48 degrees and 10 minutes.
- Regular quadrangular pyramid
How many square meters are needed to cover the shape of a regular quadrangular pyramid base edge of 10 meters if the deviation lateral edges from the base plane are 68°? Calculate waste 10%.
How high is the airplane's pilot to see 0.001 of Earth's surface?
Calculate how much land Felix Baumgartner saw after jumping from 36 km above the ground. The radius of the Earth is R = 6378 km.
- Determine 4876
The rotating cone has a height of 72 cm and an angle at the top of 72 °. Determine the volume of the sphere.
- Cylinder horizontally
The cylinder with a diameter of 3 m and a height/length of 15 m is laid horizontally. Water is poured into it, reaching a height of 60 cm below the cylinder's axis. How many hectoliters of water is in the cylinder?
- Angle of the body diagonals
Using the vector dot product calculate the angle of the body diagonals of the cube.
- Cone side
Calculate the volume and area of the cone whose height is 10 cm, and the axial section of the cone has an angle of 30 degrees between height and the cone side.
- Pyramid - angle
Calculate the regular quadrangular pyramid's surface whose base edge measured 6 cm, and the deviation from the plane of the base's sidewall plane is 50 degrees.
- Sphere in cone
A sphere of radius 3 cm describes a cone with minimum volume. Determine cone dimensions.
- Rotation of the Earth
Calculate the circumferential speed of the Earth's surface at a latitude of 61°. Consider a globe with a radius of 6378 km.
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.