Frustum practice problems - page 2 of 3
A frustum (plural: frusta or frustums) is a geometric shape that results from cutting the top off a cone or pyramid with a plane parallel to its base. It is essentially a truncated cone or pyramid, consisting of two parallel bases (a larger base and a smaller top) connected by a curved or slanted surface.Key Features of a Frustum:
1. Bases: Two parallel polygonal or circular faces (one larger and one smaller).
2. Height (h): The perpendicular distance between the two bases.
3. Slant Height (l): The distance along the lateral (side) surface between the edges of the two bases (applies to cones and pyramids).
Types of Frustums:
1. Frustum of a Cone:
- The two bases are circles.
- The lateral surface is a curved surface.
2. Frustum of a Pyramid:
- The two bases are polygons (e.g., square, triangle).
- The lateral surface consists of trapezoidal faces.
Direction: Solve each problem carefully and show your solution in each item.
Number of problems found: 54
- 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. - Hexagon cut pyramid
Calculate the volume of a regular 6-sided cut pyramid if the bottom edge is 30 cm, the top edge is 12 cm, and the side edge length is 41 cm. - Truncated cone
Calculate the volume of a truncated cone with base radiuses r1=20 cm, r2 = 10 cm, and height v = 14 cm. - Quadrangular pyramid
Calculate the surface area and volume of a regular quadrangular pyramid: sides of bases (bottom, top): a1 = 18 cm, a2 = 6cm angle α = 60 ° (Angle α is the angle between the sidewall and the base plane.) S =? , V =?
- Truncated pyramid
The concrete pedestal in a regular quadrilateral truncated pyramid has a height of 12 cm; the pedestal edges have lengths of 2.4 and 1.6 dm. Calculate the surface of the base. - Quadrilateral 81385
A regular quadrilateral pyramid with base edge length a = 15cm and height v = 21cm is given. We draw two planes parallel to the base, dividing the height of the pyramid into three equal parts. Calculate the ratio of the volumes of the 3 bodies created. - 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 pyramid
Find the volume and surface area of a regular quadrilateral truncated pyramid if base lengths a1 = 17 cm, a2 = 5 cm, and height v = 8 cm. - Truncated pyramid Find the volume of a regular 4-sided truncated pyramid if a1 = 14 cm, a2 = 8 cm, and the angle that the side wall with the base is 42 degrees.
- 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. - 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? - 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 pyramid How many cubic meters is the volume of a regular four-sided truncated pyramid with edges of one meter and 60 cm and a high of 250 mm?
- Quadrilateral 81033 The foundations of a regular truncated quadrilateral pyramid are squares. The lengths of the sides differ by 6 dm. Body height is 7 dm. The body volume is 1813 dm³. Calculate the lengths of the edges of both bases.
- Truncated pyramid
The truncated regular quadrilateral pyramid has a volume of 74 cm3, a height v = 6 cm, and an area of the lower base 15 cm² greater than the upper base's area. Calculate the area of the upper base. - 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. - Pillar
Calculate the volume of the pillar shape of a regular tetrahedral truncated pyramid if his square has sides a = 10, b = 19, and height is h = 28. - Truncated cone 3
The surface of the truncated rotating cone S = 7697 meters square, the substructure diameter is 56m and 42m, and the height of the tang is found. - Calculate 38701
Calculate the surface and volume of the cut rotating cone with base radii of 14cm and 8cm height of 11cm.
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.Do you have homework that you need help solving? Ask a question, and we will try to solve it. Solving math problems.
