Cone practice problems - page 10 of 13
Number of problems found: 248
- Rotary cone
The volume of the rotation of the cone is 733 cm³. The angle between the side of the cone and the base angle is 75°. Calculate the lateral surface area of this cone. - 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: - 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? - Cone
If the segment of the line y = -2x +3 that lies in the first quadrant is rotated about the y-axis, a cone is formed. What is the volume of the cone? - Rotary cone
A rotary cone whose height is equal to the circumference of the base has a volume 2488 cm³. Calculate the radius of the base circle and the height of the cone. - 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? - An equilateral cone
Determine the radius and height (in centimeters) of an equilateral cone that has a volume of 1 liter. - 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.
- 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? - Ice cream maker
Ice cream maker Eda has invented a new cone in the shape of a regular four-sided pyramid, in which he will sell his ice cream. The cone will have a lateral edge length of 5 cm and a slant height of 4 cm. In order to mass-produce it in a factory, the dimen - Pyramid volume change
How does the volume of a pyramid change if we triple its height? - 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 - Rotating cone
How does the volume of the rotating cone change if: a) double the radius of the base b) We reduce the height three times c) Reduce the radius of the base five times - Roof paint consumption
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. - Cylinder in Cone Volume
A cylinder with a height equal to half the height of the cone is inscribed in the rotating cone. Find the volume ratio of both bodies. - Funnel
The funnel has the shape of an equilateral cone. Calculate the surface wetted with water if we poured into the funnel 8.1 liters of water. - 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 - Volume ratio
Calculate the volume ratio of balls circumscribed (diameter r) and inscribed (diameter ϱ) into an equilateral rotating cone. - Gravel - cone
The mound of gravel has a regular circular cone shape with a height of 3.3 meters and a base circumference of 18.85 meters. How many cubic meters of gravel are in a pile? Calculate the weight of gravel if its density is p = 640 kg/cubic m. - 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
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