Kantar AI Summit- Under Embargo till Wednesday, 24th April 2024, 4 PM, IST.pdf
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Cones and frustum slides
1.
2. What is a Cone?
๏ A solid or hollow object that tapers from a
circular or roughly circular base to a point.
3. Types of Cones
๏ Right Cone - A cone that has its apex aligned
directly above the center of its base.
๏ Oblique Cone โ A cone that has its apex not
aligned above the center of its base
Right Cone Oblique Cone
http://www.mathope
nref.com/common/a
ppletframe.html?app
let=coneoblique&wid
=600&ht=350
4. Volume of Cone
๏Formula:
Volume = ๐๐2
โ
r = radius of circular base
h = height of the cone
๏Can be used for both right and oblique
cone.
5. Total Surface Area
๏Formula:
๐๐๐ด = ๐rs + ๐๐2
= ๐๐(๐ + ๐)
r = radius of circular base
s = slant height of the cone
๏This formula CANNOT be used for oblique
cone. (There are NO formula to find TSA of
oblique cone)
6. Example 1
Find out the Volume and the
Total Surface Area of the
cone.
< Given: ๐ =
22
7
>
Volume =
1
3
๐๐2
โ
=
1
3
ร
22
7
ร 72
ร10
= 513.333๐๐3
8. What is a Conical Frustum?
๏A conical frustum is a frustum created by
slicing the top off a cone (with the cut
made parallel to the base).
9. Volume of Conical Frustum
METHOD 1
๏ Formula:
V =
๐โ
3
(๐ 2
+ ๐ ๐ + ๐2
)
h = height of the frustum
r = radius of the circular top of the frustum
R = radius of the circular base of the frustum
13. Example 3
Diagram shows cone A and
frustum B. Ratio of slant height
cone A to slant height frustum
B is 1:2 . Given that radius of
cone A is 4cm and its volume
is 16ฯ๐๐3
. Find out the
volume and the total surface
area of frustum B in terms of
ฯ.