Cone
A cone is a three-dimensional figure with one circular base. A curved surface connects the base and the vertex.
Slant Height
The distance from the top of a cone, down the side to a point on the edge of the base.
Slant Height, l = √(r2+h2)
Volume of the Cone
Volume(V) = ⅓ πr2h cubic units
Example:
Find the volume of the cone whose base radius is 6 cm and height is 12 cm.
Solution:
volume of the cone= (1/3) x (22/7) x 62 x 12
= 9504/21
= 452.57 cubic cm.
Surface Area of the Cone:
The total surface area of the cone = πrl + πr2
Or
Area = πr(l + r)
Example:
Find the total surface area of a right cone if the radius is 6 inches and the slant height is 10 inches.
Solution:
T.S.A = π(6)(10)+π(6)2
=60π+36π
=96π inches2
≈301.59 inches2
Curved Surface Area of Cone
Curved Surface Area of Cone = πrl
Example:
Find the lateral surface area of a right cone if the radius is 44 cm and the slant height is 55 cm.
Solution:
L.S.A=π(4)(5)
= 20π
≈ 62.82 cm2