A frustum is a chopped-off or truncated cone or a pyramid.
Frustum
It is the 3-dimensional solid shape formed by cutting a cone or a pyramid from the top with a plane parallel to its base.
Frustum Shape
Types
Frustum can be of 2 types, depending on the shape from where it is obtained:
Frustum of a Cone
Frustum of a Pyramid
Frustums
Popcorn containers, coffee cups, buckets, and lampshades are some common examples of frustums.
Like all other solid shapes, we can calculate the volume and surface area of a frustum.
Formulas
Volume
The general formula is:
Volume of Frustum
Let us solve an example involving the above concept.
Calculate the volume of a frustum with base areas of 81 cm2, and 121 cm2, and a height of 12 cm.
Solution:
As we know, Volume (V) =${\dfrac{1}{3}h\left( B_{1}+B_{2}+\sqrt{B_{1}B_{2}}\right)}$, here B1 = 81 cm2, B2 = 121 cm2, h = 12 cm ${\therefore V=\dfrac{1}{3}\times 12\left( 81+121+\sqrt{81\times 121}\right)}$ = 1204 cm3
Surface Area
The general formula to calculate the surface area for both frustum of a cone and a pyramid is:
Surface Area of Frustum
Lateral Surface Area (LSA) or curved surface area is the area of only the curved surface. The formula is:
Lateral Surface Area (LSA) = ${\dfrac{1}{2}\left( P_{1}+P_{2}\right)\times l}$
Find the surface area of a frustum with base areas of 64 cm2, and 144 cm2, base perimeters of 32 cm and 48 cm, and a slant height of 14 cm.
Solution:
As we know, Surface Area (SA) = ${\dfrac{1}{2}\left( P_{1}+P_{2}\right)\times l+B_{1}+B_{2}}$, here P1 = 32 cm, P2 = 48 cm, B1 = 64 cm2, B2 = 144 cm2, l = 14 cm ${\therefore SA=\dfrac{1}{2}\left(32+48\right)\times 14+64+144}$ = 768 cm2
Find the lateral area of a frustum with base perimeters of 20 cm and 28 cm, and a slant height of 9 cm.
Solution:
As we know, Lateral Surface Area (LSA) = ${\dfrac{1}{2}\left( P_{1}+P_{2}\right)\times l}$, here P1 = 20 cm, P2 = 28 cm, l = 9 cm ${\therefore LSA=\dfrac{1}{2}\left( 20+28\right)\times 9}$ = 216 cm2
i am very happy to use this website