Cone practice problems - page 11 of 13

Number of problems found: 248

Confectionery
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.
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, Jane modeled a rotating cone with a base diameter of 10 cm. How tall was Jane's cone?
Cone sphere volume
A sphere is inscribed in an equilateral cone with a base diameter of 12 cm. Calculate the volume of both bodies. What percentage of the volume of the cone is filled by the inscribed sphere?
Hourglass
An hourglass consists of two identical containers in the shape of rotational cones. For simplicity, we assume that the cones touch only at their apexes. The sand reaches to half the height of the lower cone. After turning the hourglass over, it takes exac
Martians
A sphere-shaped spaceship with a diameter of 6 m landed in the meadow. To avoid attracting attention, the Martians covered it with a roof in the shape of a regular cone. How high will this roof be so that the consumption of roofing is minimal?
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.
Statements true/false
Which of the statements is not correct: ...
Sphere
Intersect between the plane and a sphere is a circle with a radius of 60 mm. The 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.
Sphere in cone
A sphere of radius 3 cm describes a cone with minimum volume. Determine the cone's dimensions.
Cone surface radius
The cone is 12 cm high, and the radius of the figure is 9 cm. Find out its surface.
2x cone
A circular cone of height 36 cm is cut by a plane parallel to the base, dividing it into two smaller cones of equal volume. Calculate the height of the smaller cone.
Sphere and cone
Within the sphere of radius G = 33 cm, inscribe the cone with the largest volume. What is that volume, and what are the dimensions of the 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.
Frustum of a cone
A reservoir contains 28.54 m³ of water when complete. The diameter of the upper base is 3.5 m, while 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.
Sphere surface
Express in square centimeters the surface of a sphere whose radius is equal to one-quarter of the radius of the cone. The diameter of the base of the cone is 20 cm.
Cone - bases
The volume of the cut cone is V = 38000π cm³. The radius of the lower base is 10 cm larger than the radius of the upper base. Determine the radius of the base if height v = 60 cm.
Similar frustums
The upper and lower radii of a frustum of a right circular cone are 8 cm and 32 cm, respectively. If the altitude of the frustum is 10 cm, how far from the bottom base must a cutting plane be made to form two similar frustums?
The surface
The surface of a truncated rotating cone with side s = 13 cm is S = 510π cm². Find the radii of the bases when their difference in lengths is 10 cm.
Two vases
Michaela has two vases in her collection. The first vase has the shape of a cone with a base diameter of d = 20 cm; the second vase has the shape of a truncated cone with a lower base of d1 = 25 cm and a diameter of the upper base d2 = 15 cm. Which vase c

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