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How To Find Volume and Surface Area of Cones

Updated: Oct 17, 2021

In this note, you will learn:

· What are cones?

· Volume and surface area of cones

· Application questions involving volume and surface area of cones



What is a cone?



Visually, a cone is similar to a pyramid. However, a cone does not constitute as a pyramid because a pyramid must have a polygonal base as mentioned above and a cone has a circular cone instead.



Of course, one might argue that a circle is essentially a polygon with an indefinite number of sides, but a polygon is defined to have a finite number of sides and hence, a circle is NOT a polygon.



Based on geometrical terms, A cone is a three-dimensional geometric shape that thins out evenly from a flat base (typically circular) to a point called the apex or vertex (similar to a pyramid).



The three main dimensions of a cone are: the radius, the height, and the slant height. The radius of a cone is measured from the center of the circular base to any point on its circumference and the slant height of a cone is measured from any point on the circumference of the circular base to the apex or vertex of the cone.



How to find the volume of cone?


The general formula to find the volume of a cone is:


V = 1/3 π r^2 h OR V = 1/3 X Base Area X Height



where V is the volume of the cone, r is the radius of the circular base of the cone and h is the height of the cone




How to find the surface area of cone?


The general formula to find the total surface area of a cone is:


Total Area = π r l + π r^2


where l is the slant height of the cone

Note: The slant height of a cone can be found by using Pythagoras’ Theorem.


OR


Total Area = Curved surface area of cone + surface area of circular base




Application example of cones


Finding the volume of a cone


A cone has a circular base of radius 15 cm and a height of 27 cm. Find the volume of the cone.




Solution:

Volume of cone = 1/3 π r^2 h

= 1/3 π (15)^2 (27)

= 6360 cm^3 (to 3 s.f.)



Finding the total surface of a cone


A cone has a circular base of radius 10 cm and a slant height of 19 cm. Find the total surface area of the cone.




Solution:

Total surface area of cone = π r l + π r^2

= π (10)(19) + π (10)^2

= 190π + 100π

= 290π

= 911 cm^2 (to 3 s.f.)



And that’s all for today, students! Math Lobby hopes that after this article, you have a clear understanding on cones, their formulae and its application!



If you have any pending questions, please do go on to our Facebook page, Instagram or contact us directly at Math Lobby! We have certified mathematics tutors to aid you in your journey to becoming a better student!



As always: Work hard, stay motivated and we wish all students a successful and enjoyable journey with Math Lobby!






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