Cone practice problems - page 10 of 13

Number of problems found: 245

Cone in cylinder
The cylinder is an inscribed cone. Find the ratio of the volume of the cone and cylinder. Please write the ratio as a decimal number and as a percentage.
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
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?
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.
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.
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?
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
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.
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?
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.
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?
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?
Rotary cone
A rotary cone whose height is equal to the circumference of the base has a volume 2732 cm³. Calculate the radius of the base circle and the height of the cone.
An equilateral cone
Determine the radius and height (in centimeters) of an equilateral cone that has a volume of 1 liter.
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
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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