Cone practice problems - page 12 of 13

Number of problems found: 248

Cutting cone
A cone with a base radius of 10 cm and a height of 12 cm is given. At what height above the base should we divide it by a section parallel to the base so that the volumes of the two resulting bodies are the same? Express the result in cm.
Frustrum - volume, area
Calculate the surface and volume of a truncated rotating cone with base radii of 8 cm and 4 cm and a height of 5 cm.
Slant surface
The surface of the rotating cone and its base area is in the ratio 18:5. Determine the volume of the cone if its body height is 12 cm.
An Elizabethan collar
An Elizabethan collar is used to prevent an animal from irritating a wound. The angle between the opening (diameter 6 inches) with a 16-inch diameter and the side of the collar is 53 degrees. Find the surface area of the collar shown.
Truncated cone
Calculate the volume of a truncated cone with base radiuses r₁=19 cm, r₂ = 11 cm, and height v = 5 cm.
A concrete pedestal
A concrete pedestal has the shape of a right circular cone and a height of 2.5 feet. The diameters of the upper and lower bases are 3 feet and 5 feet, respectively. Determine the pedestal's lateral surface area, total surface area, and volume.
The truncated
The truncated rotating cone has bases with radii r1 = 8 cm, r2 = 4 cm, and height v = 5 cm. What is the volume of the cone from which the truncated cone originated?
Max - cone
The workshop must produce the greatest cone from the iron bar (shape = prism) with dimensions 6.2 cm, 10 cm, and 6.2 cm. a) Calculate cone volume. b) Calculate the waste.
Top-open tank
The top-open tank resembles a truncated rotating cone, standing on a smaller base. Its volume is 465 m³, and the bases' radii are 4 m and 3 m. Find the tank's depth.
Truncated cone 3
The surface of the truncated rotating cone S = 7697 meters square, the substructure diameter is 56 m and 42 m, and the height of the tang is found.
The cone
The cone has a base radius of 12 cm and a height of 20 cm. It was truncated at 6 cm from the base. We created a truncated cone - frustum. Find the radius of the base of the truncated cone.
Frustrum - volume, area
Calculate the surface and volume of the truncated cone. The radius of the smaller figure is 4 cm, the height of the cone is 4 cm, and the side of the truncated cone is 5 cm.
Cone surface volume
Calculate the surface and volume of the cut rotating cone with base radii of 14 cm and 8 cm height of 11 cm.
Truncated cone 5
The height of a cone is 7 cm, the length of a side is 10 cm, and the lower radius is 3 cm. What could be the possible answer for the upper radius of a truncated cone?
Truncated cone
Find the volume and surface area of the truncated cone if r1 = 12 cm, r2 = 5 cm, and side s = 10 cm.
Equilateral cone
We pour so much water into a container with 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?
Largest possible cone
It is necessary to make the largest possible cone from an iron rod in the shape of a prism with dimensions of 5.6 cm, 4.8 cm, and 7.2 cm. a) Calculate its volume. b) Calculate the waste.
Truncated cone
A truncated cone has bases with 40 cm and 10 cm radiuses and a height of 25 cm. Calculate its surface area and volume.
Cone and cube
About what percentage has cone with base radius r larger volume than a same high cube with square base with edge length r?
Hexagon rotation
A regular hexagon of side 6 cm is rotated at 60° along a line passing through its longest diagonal. What is the volume of the figure thus generated?

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