Cone + ratio - practice problems
Number of problems found: 23
- A cone 4
A cone with a radius of 10 cm is divided into two parts by drawing a plane through the midpoint of its axis parallel to its base. Compare the volumes of the two parts. - Ratio
The radii of the two cones are in the ratio of 5.7. Calculate the area ratio of cones that have the same height. - Cross-sections of a cone
Cone with base radius 16 cm and height 11 cm divided by parallel planes to base into three bodies. The planes divide the height of the cone into three equal parts. Determine the volume ratio of the maximum and minimum of the resulting body. - Bottles of juice
How many 2-liter bottles of juice need to buy if you want to transfer the juice to 50 pitchers' rotary cone shape with a diameter of 24 cm and a base side length of 1.5 dm? - Axial section of the cone
The axial section of the cone is an isosceles triangle in which the ratio of cone diameter to cone side is 2:3. Calculate its volume if you know its area is 314 cm square. - 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? - Circular 4690
The cone shell with a base radius of 20 cm and a height of 50 cm unfolds into a circular cutout. How big is the center angle of this cutout? - Cone side
Calculate the volume and area of the cone whose height is 10 cm, and the axial section of the cone has an angle of 30 degrees between height and the cone side. - Right circular cone
The volume of a right circular cone is 5 liters. The cone is divided by a plane parallel to the base, one-third down from the vertex to the base. Calculate the volume of these two parts of the cone. - Lateral surface area
The ratio of the area of the base of the rotary cone to its lateral surface area is 3:5. Calculate the surface and volume of the cone if its height v = 4 cm. - Cone and the ratio
The rotational cone has a height of 43 cm, and the ratio of the base surface to the lateral surface is 5: 7. Calculate the surface of the base and the lateral surface. - Cone in cube
The cube is an inscribed cone. Determine the ratio of the volume of cone and cube. Please write the ratio as a decimal number and as a percentage. - Cone in cylinder
The cylinder is an inscribed cone. Find the ratio of the volume of the cone and cylinder. Please write the ratio as a decimal number and as a percentage. - Inscribed 6155
A cylinder with a height equal to half the height of the cone is inscribed in the rotating cone. Find the volume ratio of both bodies. - 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 - Volume ratio
Calculate the volume ratio of balls circumscribed (diameter r) and inscribed (diameter ϱ) into an equilateral rotating cone. - 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. - 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? - Cutting cone
A cone with a base radius of 10 cm and a height of 12 cm is given. At what height above the base should we divide it by a section parallel to the base so that the volumes of the two resulting bodies are the same? Express the result in cm. - Determine 81311
The surface of the rotating cone and its base area is in the ratio 18:5. Determine the volume of the cone if its body height is 12 cm.
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