Pythagorean theorem + circle - practice problems - page 11 of 12
Number of problems found: 229
- Calculate 5115
In the rotating cylinder, it is given: V = 120 cm3, v = 4 cm. Calculate r, S mantle. - Angle of deviation
The surface of the rotating cone is 30 cm² (with a circle base), and its surface area is 20 cm². Calculate the deviation of this cone's side from the base's plane. - Calculate 74024
The diagonal of the axial section of the rotating cylinder is 6 cm, and its surface is 30 cm square. Calculate the radius of the base. - 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
- 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?
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