# Body volume of a cone problems

#### Number of problems found: 69

- Surface of the cone

Calculate the surface of the cone if its height is 8 cm and the volume is 301.44 cm^{3}. - Surface and volume

Find the surface and volume of the rotating cone if the circumference of its base is 62.8 m and the side is 25 m long. - Cone A2V

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

Auto sprinkled with sand to an approximately conical shape. Workers wanted to determine the volume (amount of sand) and therefore measure the base's circumference and the length of both sides of the cone (over the top). What is the sand cone's volume if t - Rotation

The right triangle with legs 11 cm and 18 cm rotate around the longer leg. Calculate the volume and surface area of the formed cone. - Cone from cube

The largest possible cone was turned from a 20 cm high wooden cube. Calculate its weight if you know that the density of wood was 850 kg/m^{3} - Sphere

Intersect between plane and a sphere is a circle with a radius of 60 mm. Cone whose base is this circle and whose apex is at the center of the sphere has a height of 34 mm. Calculate the surface area and volume of a sphere. - Castle model

The castle model has a cone-shaped roof. The cone side is 45 cm long and the base radius is 27 cm. a) What is the roof volume? b) How many dm^{2}of wallpaper is used to glue the roof, ie the cone shell? c) What is the weight of the roof if it is made of woo - Rotary bodies

The rotating cone and the rotary cylinder have the same volume 180 cm^{3}and the same height v = 15 cm. Which of these two bodies has a larger surface area? - Calculate

Calculate the surface and volume of the cone that results from the rotation of the right triangle ABC with the squares 6 cm and 9 cm long around the shorter squeegee. - A concrete pedestal

A concrete pedestal has a shape of a right circular cone having a height of 2.5 feet. The diameter of the upper and lower bases are 3 feet and 5 feet, respectively. Determine the lateral surface area, total surface area, and the volume of the pedestal. - Gravel - cone

The mound of gravel has a regular circular cone shape with a height 3.3 meter and a base circumference of 18.85 meters. How many cubic meters of gravel is in a pile? Calculate the weight of gravel if its density is p = 640 kg / cubic m. - Frustum of a cone

A reservoir contains 28.54 m^{3}of water when full. The diameter of the upper base is 3.5 m, while at the lower base is 2.5 m. Find the height if the reservoir is in the form of a frustum of a right circular cone. - 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. - From plasticine

Michael modeled from plasticine a 15 cm high pyramid with a rectangular base with the sides of the base a = 12 cm and b = 8 cm. From this pyramid, Janka modeled a rotating cone with a base diameter d = 10 cm. How tall was Janka's cone? - Truncated cone

Calculate the height of the rotating truncated cone with volume V = 794 cm^{3}and a base radii r_{1}= 9.9 cm and r_{2}= 9.8 cm. - Equilateral cone

We pour so much water into a container that has the shape of an equilateral cone, the base of which has a radius r = 6 cm, that one-third of the volume of the cone is filled. How high will the water reach if we turn the cone upside down?

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