Cone practice problems - page 10 of 13
Number of problems found: 245
- Rotary bodies
The rotating cone and the rotary cylinder have the same volume of 180 cm³ and the same height, v = 15 cm. Which of these two bodies has a larger surface area? - Rotary cone
A 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 the height of the cone. - Ice cream maker
Ice cream maker Eda has invented a new nice cone in the shape of a regular four-sided pyramid, in which he will sell his ice cream. The cone will have a side edge length of 5 cm and a wall height of 4 cm. In order to mass-produce it in the factory, they s - Cone
If the segment of the line y = -3x +4 that lies in the first quadrant is rotated about the y-axis, a cone is formed. What is the volume of the cone? - 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 - The funnel
The funnel has the shape of an equilateral cone. If you pour 3 liters of water into the funnel, calculate the area wetted with water. - Pyramid 7903
How does the volume of a pyramid change if we triple its height?
- Wooden bowls
Twenty wooden bowls in the shape of a truncated cone should be painted on the outside and inside with wood varnish. We need 0.1 l of paint to paint 200 cm². How many liters of paint do we have to buy if the bowls are 25 cm high, the bottom of the bowl has - Confectionery 7318
The confectioner needs to carve a cone-shaped decoration from a ball-shaped confectionery mass with a radius of 25 cm. Find the radius of the base of the ornament a (and the height h). He uses as much material as possible is used to make the ornament. - 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? - Sphere in cone
A sphere of radius 3 cm describes a cone with minimum volume. Determine cone dimensions. - Consumption 15663
The cone-shaped sheet metal roof has a base diameter of 80 cm and a height of 60 cm. If 1 kg of paint is consumed per 6 m² of sheet metal, calculate the paint consumption for painting this roof. - Right-angled trapezoid
A right-angled trapezoid with the measure of the acute angle of 50° is given. The lengths of its bases are 4 and 6 units. The volume of the solid obtained by rotation of the given trapezoid about the longer base is: - The cone
The cone's lateral surface area is 4 cm², and the area of the base is 2 cm². Find the angle in degrees (deviation) of the cone sine and the cone base plane. (The cone side is the segment joining the vertex cone with any point of the base circle. All sides - 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 of 10 cm. How tall was Janka's cone?
- Truncated cone
Calculate the height of the rotating truncated cone with volume V = 1471 cm³ and a base radii r1 = 6.1 cm and r2 = 7.9 cm. - Volume ratio
Calculate the volume ratio of balls circumscribed (diameter r) and inscribed (diameter ϱ) into an equilateral rotating cone. - Cone
The rotating cone volume is 9.42 cm3, with a height of 10 cm. What angle is between the side of the cone and its base? - Vertex angle - cone
The rotating cone has a height of 72 cm and an angle at the top of 72°. Determine the volume of a sphere with the same radius as the cone. - Cylindrical rod
We should grind a cylindrical rod with a diameter of 6 cm and a length of 20 cm to form a conical rod of the same size and the same base diameter. What will be the volume of material removed?
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