# Cone - math word problems

- Right circular cone

The volume of a right circular cone is 5 liters. Calculate the volume of the two parts into which the cone is divided by a plane parallel to the base, one-third of the way down from the vertex to the base. - Axial section

Axial section of the cone is an equilateral triangle with area 208 dm^{2}. Calculate the volume of the cone. - Cone A2V

Surface of cone in the plane is a circular arc with central angle of 126° and area 415 cm^{2}. Calculate the volume of a cone. - Cone

Calculate volume and surface area of the cone with diameter of the base d = 15 cm and side of cone with the base has angle 52°. - Cone

Circular cone of height 15 cm and volume 5699 cm^{3}is at one-third of the height (measured from the bottom) cut by a plane parallel to the base. Calculate the radius and circumference of the circular cut. - Sandpile

Auto sprinkled with sand to an 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 san - Rotation

The right triangle with legs 14 cm and 20 cm rotate around the longer leg. Calculate the volume and surface area of the formed cone. - Cap

Jesters hat is shaped a rotating cone. Calculate how much paper is needed to the cap 60 cm high when head circumference is 52 cm. - Rotary cone

The volume of the rotation of the cone is 472 cm^{3}and angle between the side of the cone and base angle is 70°. Calculate lateral surface area of this cone. - Cone

Circular cone with height h = 29 dm and base radius r = 3 dm slice plane parallel to the base. Calculate distance of the cone vertex from this plane, if solids have the same volume. - Tower

How many m^{2}of copper plate should be to replace roof of the tower conical shape with diameter 24 m and the angle at the vertex of the axial section is 144°? - Canopy

Mr Peter has metal roof cone shape with a height of 127 cm and radius 130 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 3.3 m^{2}? - Rotary cone

Rotary cone whose height is equal to the circumference of the base, has a volume 229 cm^{3}. Calculate the radius of the base circle and height of the 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. - Cut and cone

Calculate the volume of the rotation cone which lateral surface is circle arc with radius 15 cm and central angle 63 degrees. - Rotating cone

Calculate volume of a rotating cone with base radius r=12 cm and height h=7 cm. - Truncated cone

Calculate the height of the rotating truncated cone with volume V = 1115 cm^{3}and a base radii r_{1}= 7.9 cm and r_{2}= 9.7 cm. - Sphere in cone

A sphere of radius 3 cm desribe cone with minimum volume. Determine cone dimensions. - Rotating cone II

Calculate area of surface of rotating cone with base radius r=19 cm and height h=9 cm. - Cone and the ratio

Rotational cone has a height 23 cm and the ratio of the base surface to lateral surface is 7: 9. Calculate a surface of the base and the lateral surface.

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