Answer :
Given:
The diagram of a cone.
To find:
The lateral area, surface area and volume of the cone.
Solution:
From the given diagram, we get
Radius of the cone = 6
Slant height of the cone = 10
Suppose [tex]h[/tex] be the height of the cone.
According to Pythagoras theorem:
[tex]hypotenuse^2=Perpendicular^2+Base^2[/tex]
Using the Pythagoras theorem, we get
[tex]10^2=(6)^2+h^2[/tex]
[tex]100=36+h^2[/tex]
[tex]100-36=h^2[/tex]
[tex]64=h^2[/tex]
Taking square root on both sides, we get
[tex]\sqrt{64}=h[/tex]
[tex]8=h[/tex]
The lateral area of a cone is:
[tex]A_L=\pi rl[/tex]
[tex]A_L=\pi (6)(8)[/tex]
[tex]A_L=48\pi[/tex]
The surface area of a cone is:
[tex]A_S=\pi rl+\pi r^2[/tex]
[tex]A_S=\pi (6)(8)+\pi (6)^2[/tex]
[tex]A_S=48\pi +36\pi[/tex]
[tex]A_S=84\pi[/tex]
Volume of cone is:
[tex]V=\dfrac{1}{3}\pi r^2h[/tex]
[tex]V=\dfrac{1}{3}\pi (6)^2(8)[/tex]
[tex]V=\dfrac{288}{3}\pi [/tex]
[tex]V=96\pi [/tex]
Hence, the lateral area of a cone is [tex]48\pi[/tex] sq. units, the surface area of a cone is [tex]84\pi[/tex] sq. units and the volume of the cone is [tex]96\pi[/tex] cubic units.
