# Problems of the right triangle

#### Number of problems found: 1300

- Pyramid cut

We cut the regular square pyramid with a parallel plane to the two parts (see figure). The volume of the smaller pyramid is 20% of the volume of the original one. The bottom of the base of the smaller pyramid has a content of 10 cm^{2}. Find the area of the - Earth's circumference

Calculate the Earth's circumference of the parallel 48 degrees and 10 minutes. - Circular pool

The base of the pool is a circle with a radius r = 10 m, excluding a circular segment that determines the chord length 10 meters. The pool depth is h = 2m. How many hectoliters of water can fit into the pool? - Hexagon cut pyramid

Calculate the volume of a regular 6-sided cut pyramid if the bottom edge is 30 cm, the top edge is 12 cm, and the side edge length is 41 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. - Conical bottle

When a conical bottle rests on its flat base, the water in the bottle is 8 cm from its vertex. When the same conical bottle is turned upside down, the water level is 2 cm from its base. What is the height of the bottle? - 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. - 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? - 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. - 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. - Airplane

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

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

Find the position of the center of gravity of a system of four mass points having masses, m_{1}, m_{2}= 2 m1, m_{3}= 3 m1, and m_{4}= 4 m_{1}, if they lie at the vertices of an isosceles tetrahedron. (in all cases, between adjacent material points, the distance - Angle of the body diagonals

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

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

4 m long ladder touches the cube 1mx1m at the wall. How high reach on the wall? - 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).

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