Frustum practice problems - last page
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
- 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? - A sphere
A sphere has a radius of 5.5 cm. Determine its volume and surface area. A frustum of the sphere is formed by two parallel planes. One through the diameter of the curved surface of the frustum is to be of the surface area of the sphere. Find the height and - 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. - Quadrilateral 5814
Calculate the surface area and volume of a regular quadrilateral truncated pyramid if the base edges are 87 cm and 64 cm and the wall height is 49 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. - 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? - 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 40 cm and 10 cm radiuses and a height of 25 cm. Calculate its surface area and volume. - Quadrilateral 58663
They melted the steel part in the shape of a truncated quadrilateral needle and produced three identical cubes. Determine the surface area of one cube if the edges of the bases of the pyramid are 30 mm and 80 mm and the pyramid's height is 60 mm. I don't
- 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 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.
- Truncated 12391
A sphere is inscribed into a truncated cone and touches both the base and the mantle. The base diameter of the cone is D. What is its diameter? - 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.
We apologize, but in this category are not a lot of examples.
Do you have homework that you need help solving? Ask a question, and we will try to solve it. Solving math problems.
Do you have homework that you need help solving? Ask a question, and we will try to solve it. Solving math problems.
