Pythagorean theorem + circle - practice problems - page 11 of 12
Number of problems found: 227
- Cone-shaped 44161
How many square meters of roofing is needed to cover the cone-shaped roof, if the perimeter of its base is 15.7m and a height of 30dm - Triangular 6610
The shell of the rotating cylinder is four times larger than the contents of its base. Determine the volume of the regular triangular prism inscribed in the cylinder. The radius of the bottom of the cylinder is 10 cm. - Metal balls
Four metal balls with a diameter of 5 cm are placed in a measuring cylinder with an inner diameter of 10 cm. What is the smallest water volume to be poured into the cylinder so that all balls are below the water level? - Axial section
The axial section of the cylinder has a diagonal 36 cm long, and we know that the area of the side and the base area is in ratio 1:1. Calculate the height and radius of the cylinder base.
- Elevation
What must be an observer's elevation so that he may see an object on the Earth 536 km away? Assume the Earth to be a smooth sphere with a radius 6378.1 km. - Intersection 40981
The intersection of a plane is 2 cm from the sphere's center, and this sphere is a circle whose radius is 6 cm. Calculate the surface area and volume of the sphere. - Sphere parts, segment
A sphere with a diameter of 20.6 cm, the cut is a circle with a diameter of 16.2 cm. What are the volume of the segment and the surface of the segment? - Truncated cone 6
Calculate the volume of the truncated cone whose bases consist of an inscribed circle and a circle circumscribed to the opposite sides of the cube with the edge length a=1. - Cap
A rotating cone shapes a jesters hat. Calculate how much paper is needed for the cap 54 cm high when the head circumference is 47 cm.
- Truncated cone 3
The surface of the truncated rotating cone S = 7697 meters square, the substructure diameter is 56m and 42m, find the height of the tang. - Hexagonal 13891
A regular hexagonal pyramid has a base inscribed in a circle with a radius of 8 cm and a height of 20 cm. Please sketch the picture. Please calculate the surface of a regular hexagonal pyramid. - Spherical cap
Calculate the volume of the spherical cap and the areas of the spherical canopy if r = 5 cm (radius of the sphere), ρ = 4 cm (radius of the circle of the cap). - 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.
- 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. - Horizon
The top of a lighthouse is 19 m above the sea. How far away is an object just "on the horizon"? [Assume the Earth is a sphere of radius 6378.1 km.] - Hexagonal 8200
The tops of the base of a regular hexagonal pyramid lie on a circle with a radius of 10 cm. The height of the pyramid is 12cm. What is its volume? - Axial section
The axial section of the cylinder has a diagonal 40 cm. The shell size and base surface are in the ratio 3:2. Calculate the volume and surface area of this cylinder. - Quadrilateral 83307
The diagonal of section DBFH of the regular quadrilateral prism ABCDEFGH inscribes a circle with a diameter of 8 cm. What is the volume of the prism?
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