Cone + area - practice problems - last page
Number of problems found: 140
- Equilateral 81222
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? - 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? - Surface 64744
The cone is 12 cm high, and the radius of the figure is 9 cm. Find out its surface. - One-quarter 46001
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.
- 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. - 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 10cm. - 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 a truncated rotating cone with base radii of 8 cm and 4 cm and a height of 5 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.
- Determine 81311
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. - 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. - Truncated cone 3
The surface of the truncated rotating cone S = 7697 meters square, the substructure diameter is 56m and 42m, find the height of the tang. - 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. - 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. - 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? - Lamp cone
Calculate the surface of a lampshade shaped like a rotary truncated cone with a base diameter of 32 cm and 12 cm and a height of 24 cm.
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