Write all the formula of cone?
Answers
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Step-by-step explanation:
Cone Formula
The cone has two formula one for its surface area and one for its volume (because it is a 3D shape). Now, let’s discuss the formula
The surface area of the cone
If we talk about the surface area of the cone then it is the sum of all lateral side and the base of the cone. Moreover, the cone somewhat resembles a pyramid so the formula of the surface area is related.
Cone surface area = πrs+πr2
Derivation of the Formula
r = refers to the radius of the circular base
s = refers to the slant height of the cone
π = refers to the value of pi
The volume of the Cone
The cone has a volume which means it is a 3D shape. Also, the curved surface of the cone joins the apex and base of the cone. Moreover, having volume means that it occupies space. Furthermore, we measure it in a cubic meter.
Besides, finding the volume be sure that all the units are in the same unit.
Volume of the cone = 13πr2h
Derivation of the Formula
π = refers to the value of pi
r = refers to the radius of the circular base
h = is the height of the cone
13 = refers to the value of the one-third value
Besides, the volume of the cone and a cylinder are somewhat related to each other. So, do the volume of prism and pyramid. Besides, if the height of the cylinder and cone are equal then the volume of the cylinder will be three times (3×) the volume of the cone.
Solved Example on Cone Formula
Example 1
Find the surface area of the cone whose radius is 4 cm and slant height is 8 cm?
Solution:
Surface area of a cone = πrs+πr2
A = (3.14 × 4 × 8) + (3.14 × 4 × 4)
A = 100.48 + 50.24 = 15.72 cm2
So, the surface area of the cone of radius 4 cm and slant height 8 cm is 15.72 cm2.
Example 2
Find the volume of the cone whose radius is 8 cm and height is 18 cm?
Solution:
Volume of the cone = 13πr2h
V = 13 × 3.14 × 8 × 8 × 18
V = 13 × 3617.28 = 1206.4 cm3
The volume of the cone is 1206.4 cm3