What is a Frustum in Geometry?
What is a Frustum?
A frustum is a geometric shape that is created when a pyramid or cone is cut off at an angle. The shape that is created is called a frustum. It is the result of cutting off the top of a pyramid or cone, leaving a section with a smaller base and a larger top.
The most common type of frustum is a pyramid frustum, which is created when the top of a pyramid is cut off. This will create a shape that looks like a pyramid with a flat top. The other type of frustum is a conical frustum, which is created when the top of a cone is cut off. This will create a shape that looks like a cone with a flat top.
Frustum Definition
The technical definition of a frustum is a polyhedron that is created when the top of a pyramid or cone is cut off at an angle. The resulting shape is a frustum. It is the result of cutting off the top of a pyramid or cone, leaving a section with a smaller base and a larger top.
The most common type of frustum is a pyramid frustum, which is created when the top of a pyramid is cut off. This will create a shape that looks like a pyramid with a flat top. The other type of frustum is a conical frustum, which is created when the top of a cone is cut off. This will create a shape that looks like a cone with a flat top.
Frustum Volume and Area
The volume and area of a frustum can be calculated using various formulas. For a pyramid frustum, the volume can be calculated using the formula V= 1/3Ah, where A is the area of the base and h is the height of the frustum. For a conical frustum, the volume can be calculated using the formula V= 1/3pr2h, where r is the radius of the base and h is the height of the frustum.
The area of a frustum can be calculated using the formula A=pr2+prs+pr2, where r is the radius of the base and s is the slant length of the frustum. The slant length is the distance from the center of the base to the top of the frustum.
Practice Problems
1. Find the volume of a pyramid frustum with a base area of 12 cm2 and a height of 8 cm.
Answer: 96 cm3
2. Find the volume of a conical frustum with a base radius of 3 cm and a height of 6 cm.
Answer: 84 cm3
3. Find the area of a pyramid frustum with a base area of 16 cm2, a slant length of 10 cm, and a height of 7 cm.
Answer: 180 cm2
4. Find the area of a conical frustum with a base radius of 4 cm, a slant length of 9 cm, and a height of 8 cm.
Answer: 264 cm2
5. Find the volume of a pyramid frustum with a base area of 10 cm2 and a slant length of 12 cm.
Answer: 60 cm3
6. Find the volume of a conical frustum with a base radius of 5 cm and a slant length of 15 cm.
Answer: 150 cm3
Summary
A frustum is a geometric shape that is created when a pyramid or cone is cut off at an angle. The most common type of frustum is a pyramid frustum, which is created when the top of a pyramid is cut off. The other type of frustum is a conical frustum, which is created when the top of a cone is cut off. The volume and area of a frustum can be calculated using various formulas. The formulas for calculating the volume and area of a frustum are provided in this article. Finally, several practice problems have been provided to help you practice calculating the volume and area of a frustum.
FAQ
What is the frustum formula?
The frustum formula is derived from the volume of a right circular cone: V = 1/3pr2h, where r is the radius of the base and h is the height of the cone.
Is frustum a geometric shape?
Yes, a frustum is a type of geometric shape that is formed when the top portion of a cone or pyramid is cut off. It is the portion of a cone or pyramid between the top and bottom bases.
What are the properties of frustum?
The properties of frustum include its height, the upper and lower base radii, and the included angle between the two bases. It also has two lateral surfaces and an upper and lower base.
What is frustum in mensuration?
In mensuration, a frustum is a three-dimensional shape formed from the truncation of a solid (such as a cone or pyramid). It has two parallel bases, an upper base and a lower base, and a curved surface connecting the two. The height of the frustum is the distance between the two bases.