Practice problems of the volume of a cone - last page
Number of problems found: 156
- Deviation 70434
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 has the shape of a truncated rotating cone, which stands on a smaller base. The tank's volume is 465 m3, and the radii of the bases are 4 m and 3 m. Find the depth of the tank. - 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. - 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.
- 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
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. - Truncated cone
A truncated cone has bases with radiuses 40 cm and 10 cm 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? - 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 of 14 cm. The altitude is 30 cm. Determine the weight in kg if the wood density is 10 grams/cm³. - Cylinder-shaped 81512
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? - Truncated cone 6
Calculate the volume of the truncated cone whose bases consist of an inscribed circle and a circle circumscribed to the opposite sides of the cube with the edge length a=1.
- Sphere submerged in the cone
A right circular cone with a top width of 24 cm and an altitude of 8 cm is filled with water. A spherical steel ball with a radius of 3.0cm is submerged in the cone. Find the volume of water below the sphere. - Determine 46401
The volume of the sphere is 20% larger than the volume of the cone. Find its surface if the volume of the cone is 320 cm³.
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