Cone - examples
- Axial section
Axial section of the cone is equilateral triangle with area 300 m2. Calculate volume of the cone.
- Cone A2V
Surface of cone in the plane is a circular arc with central angle of 126° and area 415 cm2. Calculate the volume of a cone.
Calculate volume and surface area of the cone with diameter of the base d = 12 cm and side of cone with the base has angle 41°47'59″.
Circular cone of height 16 cm and volume 5024 cm3 is at third of the height (measured from the bottom) cut plane parallel to base. Calculate the radius and circumference of the circular cut.
- Sand pile
Auto sprinkled with sand to approximately conical shape. Workers wanted to determine the volume (amount of sand) and therefore measure the circumference of the base and the length of both sides of the cone (over the top). What is the volume of the sand c
Right triangle with legs 9 cm and 16 cm rotate around longer leg. Calculate the volume and surface area of the formed cone.
Jesters hat is shaped a rotating cone. Calculate how much paper is needed to the cap 50 cm high when head circumference is 47 cm.
- Rotary cone
The volume of the rotation of the cone is 104 cm3 and angle between the side of the cone and base angle is 80°. Calculate lateral surface area of this cone.
How many m2 of copper plate should be to replace roof of the tower conical shape with diameter 13 m and the angle at the vertex of the axial section is 150°?
Mr Peter has metal roof cone shape with a height of 36 cm and radius 73 cm over well. He needs paint the roof with anticorrosion. How many kg of color must he buy if the manufacturer specifies the consumption of 1 kg to 2.1 m2?
- Rotary cone
Rotary cone whose height is equal to the circumference of the base, has a volume 4772 cm3. Calculate the radius of the base circle and height of the cone.
- Cut and cone
Calculate the volume of the rotation cone which lateral surface is circle arc with radius 14 cm and central angle 66 degrees.
Circular cone with height h = 11 dm and base radius r = 4 dm slice plane parallel to the base. Calculate distance of the cone vertex from this plane, if solids have the same volume.
- 2x cone
Circular cone height 60 cm was cut plane parallel with base. Volume of these two small cones is the same. Calculate the height of the smaller cone.
- Rotating cone
Calculate volume of a rotating cone with base radius r=7 cm and height h=17 cm.
- Rotating cone II
Calculate area of surface of rotating cone with base radius r=7 cm and height h=17 cm.
- Cone and the ratio
Rotational cone has a height 28 cm and the ratio of the base surface to lateral surface is 4: 7. Calculate a surface of the base and the lateral surface.
- Truncated cone
Calculate the height of the rotating truncated cone with volume V = 1299 cm3 and a base radii r1 = 6.3 cm and r2 = 9.7 cm.
- Sphere in cone
A sphere of radius 3 cm desribe cone with minimum volume. Determine cone dimensions.
- Sphere and cone
Within the sphere of radius G = 26 cm inscribe cone with largest volume. What is that volume and what are the dimensions of the cone?