Pythagorean theorem + angle - practice problems - last page
Number of problems found: 259
- Maximum of volume
The shell of the cone is formed by winding a circular section with a radius of 1. For what central angle of a given circular section will the volume of the resulting cone be maximum? - Hexagonal pyramid
Calculate the surface area of a regular hexagonal pyramid with a base inscribed in a circle with a radius of 8 cm and a height of 20 cm. - 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. - Cuboid
Cuboid ABCDEFGH with 10 cm height has a base edge length 6 cm and 8 cm. Determine the angle between the body diagonal and the base plane (round to degrees).
- Cone
Calculate the volume and surface area of the cone with a diameter of the base d=15 cm and the side of the cone with the base has angle 52°. - Side edges
The regular 4-sided pyramid has a body height of 2 dm, and the opposite side edges form an angle of 70°. Calculate the surface area and volume of the pyramid. - The hemisphere
The hemisphere container is filled with water. What is the radius of the container when 10 liters of water pour from it when tilted 30 degrees? - Hexagonal pyramid
The pyramid's base is a regular hexagon, which can be circumscribed in a circle with a radius of 1 meter. Calculate the volume of a pyramid 2.5 meters high. - Tetrahedral pyramid
What is the surface of a regular tetrahedral (four-sided) pyramid if the base edge a=16 and height v=16?
- Wall height
Calculate the height of a regular hexagonal pyramid with a base edge of 5 cm and a wall height w = 20 cm. - Hexagon
Calculate the regular hexagonal prism's surface whose base edge a = 12cm and side edge b = 3 dm. - Regular hexagonal pyramid
Calculate the height of a regular hexagonal pyramid with a base edge of 5 cm and a wall height of w = 20cm. Sketch a picture. - Triangular prism
Calculate the surface of a regular triangular prism; the base's edges are 6 cm long, and the height of the prism is 15 cm. - Cut and cone
Calculate the volume of the rotation cone whose lateral surface is a circular arc with radius 15 cm and central angle 63 degrees.
- Hexagonal 6424
Calculate the volume and surface of a regular hexagonal prism, the base edge of which is 5 cm long and its height is 20 cm. - Hexa prism
Determine the volume of the hex prism with an edge base of 4 cm. The body height is 28 cm. - Angle of the body diagonals
Using the vector dot product calculate the angle of the body diagonals of the cube. - Box
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.
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