Cone practice problems - page 12 of 13

Number of problems found: 245

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?
Truncated cone
Find the volume and surface area of the truncated cone if r1 = 12 cm, r2 = 5 cm, and side s = 10 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.
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?
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.
Truncated cone
Calculate the volume of a truncated cone with base radiuses r₁=19 cm, r₂ = 11 cm, and height v = 5 cm.
Side deviation
Frustum has the base radii of the figures r1 and r2: r1> r2, r2 = s, and if the side deviation from the base plane is 60°. Express the surface and volume of the cone frustum using its side s.
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.
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.
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?
Calculate 38701
Calculate the surface and volume of the cut rotating cone with base radii of 14cm and 8cm height of 11cm.
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.
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.
Truncated cone 5
The height of a cone is 7 cm, the length of a side is 10 cm, and the lower radius is 3cm. What could be the possible answer for the upper radius of a truncated cone?
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?
Calculate 45991
Calculate the radius of a sphere with the same volume as a cone with a radius of 5cm and a height of 7cm.
Heptagonal pyramid
A hardwood for a column is in the form of a frustum of a regular heptagonal pyramid. The lower base edge is 18 cm, and the upper base is 14 cm. The altitude is 30 cm. Determine the weight in kg if the wood density is 10 grams/cm³.
Cylinder-shaped part
A truncated cone-shaped part with base radii of 4 cm and 22 cm is to be recast into a cylinder-shaped part of the same height as the original part. What base radius will the new part have?

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