Number of problems found: 120
- The cone
The lateral surface area of the cone is 4 cm2, the area of the base of the cone is 2 cm2. Determine 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 c
- Sphere in cone
A sphere of radius 3 cm describes a cone with minimum volume. Determine cone dimensions.
- Hard cone problem
The surface of the cone is 200 cm², its height is 7 centimeters. Calculate the volume of this cone.
- Cone in cube
The cube is inscribed cone. Determine the ratio of the volume of cone and cube. The ratio express as a decimal number and as percentage.
- Cone in cylinder
The cylinder is inscribed cone. Determine the ratio of the volume of cone and cylinder. The ratio express as a decimal number and as percentage.
- The volume
The volume of the rotating cone is 376.8cm³, the height of this cone is 1dm. Calculate the diameter of the cone base.
If the segment of the line y = -3x +4 that lies in quadrant I is rotated about the y-axis, a cone is formed. What is the volume of the cone?
- Rotary cone
The volume of the rotation of the cone is 472 cm3 and angle between the side of the cone and base angle is 70°. Calculate lateral surface area of this cone.
- Cone and cube
About what percentage hase cone with base radius r larger volume than same high cube with square base with edge length r?
- 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.
- Angle of cone
The cone has a base diameter of 1.5 m. The angle at the main apex of the axial section is 86°. Calculate the volume of the cone.
- 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?
- The cone
The cone with a base radius of 12 cm and a height of 20 cm was truncated at a distance of 6 cm from the base, thus creating a truncated cone. Find the radius of the base of the truncated cone.
- 2x cone
Circular cone height 84 cm was cut plane parallel with base. Volume of these two small cones is the same. Calculate the height of the smaller cone.
- Ice cream in cone
In the ice cream cone with a diameter of 5.7 cm is 0.8 dl of ice cream. Calculate the depth of the cone.
Circular cone with 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.
- Rotary cone
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 height of the cone.
- The rotating
The rotating cone has a height of 0.9 m and the diameter of the base is 7.2 dm. Calculate the surface of the cone. (Hint: use Pythagorean theorem for a side of cone)
Into rotating cone with dimensions r = 8 cm and h = 8 cm incribe cylinder with maximum volume so that the cylinder axis is perpendicular to the axis of the cone. Determine the dimensions of the cylinder.
- Rotating cone
The rotating cone has a base diameter of 18 dm and a height of 12 dm. Calculate the volume V.