Cone + circle - practice problems - page 2 of 3
Number of problems found: 46
- Slant height
The cone's slant height is 5cm, and the radius of its base is 3cm, so find the cone's volume. - 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. - Surface and volume
Find the surface and volume of the rotating cone if the circumference of its base is 62.8 m and the side is 25 m long. - Rotating 7947
In the rotating cone = 100π S rotating cone = 90π v =? r =? - Circumference 23311
Calculate the circumference of the cone base; round the result to millimeters. If you know: radius 24 mm and height 46 mm. - Volume of cone
Find the volume of a right circular cone-shaped building with a height of 9 m and a radius base of 7 m.
- 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. - 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 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 - The cone
The cone's lateral surface area is 4 cm², and the area of the base is 2 cm². Find the angle in degrees (deviation) of the cone sine and the cone base plane. (Cone side is the segment joining the vertex cone with any point of the base circle. All sides of - From plasticine
Michael modeled from plasticine a 15 cm high pyramid with a rectangular base with the sides of the base a = 12 cm and b = 8 cm. From this pyramid, Janka modeled a rotating cone with a base diameter d = 10 cm. How tall was Janka's cone?
- Truncated cone
Calculate the height of the rotating truncated cone with volume V = 1354 cm³ and a base radii r1 = 9.1 cm and r2 = 5.4 cm. - One-quarter 46001
Express in square centimeters the surface of a sphere whose radius is equal to one-quarter of the radius of the cone. The diameter of the base of the cone is 20 cm. - Sphere
Intersect between the plane and a sphere is a circle with a radius of 60 mm. The cone, whose base is this circle and whose apex is at the center of the sphere, has a height of 34 mm. Calculate the surface area and volume of a sphere. - Two vases
Michaela has two vases in her collection. The first vase has the shape of a cone with a base diameter d = 20 cm; the second vase has the shape of a truncated cone with the lower base d1 = 25 cm and the diameter of the upper base d2 = 15 cm. Which vase can - Similar frustums
The upper and lower radii of a frustum of a right circular cone are 8 cm and 32 cm, respectively. If the altitude of the frustum is 10 cm, how far from the bottom base must a cutting plane be made to form two similar frustums?
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