Equation + cone - practice problems
Number of problems found: 16
- Sphere in cone
A sphere of radius 3 cm describes a cone with minimum volume. Determine cone dimensions. - Hard cone problem
The cone's surface is 200 cm², and its height is 7 centimeters. Calculate the volume of this cone. - Rotating 7947
In the rotating cone = 100π S rotating cone = 90π v =? r =? - The surface
The surface of a truncated rotating cone with side s = 13 cm is S = 510π cm². Find the radii of the bases when their difference in lengths is 10cm. - 2x cone
Circular cone height 84 cm was cut plane parallel with the base. The volume of these two small cones is the same. Calculate the height of the smaller cone. - Determine 73454
The volume of the cut cone is V = 38000π cm³. The radius of the lower base is 10 cm larger than the radius of the upper base. Determine the radius of the base if height v = 60 cm. - 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 and cone
Within the sphere of radius G = 33 cm, inscribe the cone with the largest volume. What is that volume, and what are the dimensions of the cone? - Saleswoman 37041
The saleswoman mixed two types of candies into the cone. Half a kilo of fruit at 90 CZK per kilogram and 400 g of nut at 117 CZK per kilogram. How many crowns will 1 kg of this mixture cost? - The truncated
The truncated rotating cone has bases with radii r1 = 8 cm, r2 = 4 cm and height v = 5 cm. What is the volume of the cone from which the truncated cone originated? - Conical bottle
When a conical bottle rests on its flat base, the water in the bottle is 8 cm from its vertex. When the same conical bottle is turned upside down, the water level is 2 cm from its base. What is the height of the bottle? - 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. - 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? - Cylinder-shaped 81512
A truncated cone-shaped part with base radii of 4 cm and 22 cm is to be recast into a cylinder-shaped part of the same height as the original part. What base radius will the new part have? - Something 5385
Janko got pocket money and wants to buy something good for it. If he purchased four cakes, it would increase by 0.50 euros. If he wanted to buy five cakes, he would miss 0.60 euros. He would spend all his pockets on the rest if he bought two cakes and thr - 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.
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