Cone - high school - practice problems - page 3 of 5
Number of problems found: 88
- Axial section
The axial section of the cone is an equilateral triangle with an area 208 m². Calculate the volume of the cone. - Circumference 3370
Calculate the surface and volume of the rotating cone, whose base circumference is 125.6 cm and the side is 25 cm long. - 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. - Calculate 8326
Calculate the cone shell with a base diameter of 40 cm and a cone height of 50 cm.
- Semicircle 82687
If the shell of a cone is a semicircle, then the diameter of the cone's base is equal to its side's length. Prove it. - Resulting 4446
A square with a side length of 3 cm rotates around its diagonal. Calculate the volume and surface area of the resulting body. - Rotating 7947
In the rotating cone = 100π S rotating cone = 90π v =? r =? - Cone
The circular cone has height h = 29 dm and base radius r = 3 dm slice plane parallel to the base. Calculate the distance of the cone vertex from this plane if solids have the same volume. - Cone
Into rotating cone with dimensions r = 8 cm and h = 8 cm is an inscribed cylinder with maximum volume so that the cylinder axis is perpendicular to the cone's axis. Determine the dimensions of the cylinder.
- Rotary cone
The volume of the rotation of the cone is 472 cm³. The angle between the side of the cone and the base angle is 70°. Calculate the lateral surface area of this cone. - Rotary bodies
The rotating cone and the rotary cylinder have the same volume of 180 cm³ and the same height, v = 15 cm. Which of these two bodies has a larger surface area? - Cone
If the segment of the line y = -3x +4 that lies in the first quadrant is rotated about the y-axis, a cone is formed. What is the volume of the cone? - Rotary cone
A rotary cone whose height is equal to the circumference of the base has a volume 229 cm³. Calculate the radius of the base circle and the height of the cone. - The funnel
The funnel has the shape of an equilateral cone. Calculate the area wetted with water if you pour 3 liters of water into the funnel.
- 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? - Sphere in cone
A sphere of radius 3 cm describes a cone with minimum volume. Determine cone dimensions. - 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 - Right-angled trapezoid
A right-angled trapezoid with the measure of the acute angle of 50° is given. The lengths of its bases are 4 and 6 units. The volume of the solid obtained by rotation of the given trapezoid about the longer base is: - Confectionery 7318
The confectioner needs to carve a cone-shaped decoration from a ball-shaped confectionery mass with a radius of 25 cm. Find the radius of the base of the ornament a (and the height h). He uses as much material as possible is used to make the ornament.
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