The slant height of a right circular cone is 15m and its height is 9m. The area of its curved surface is:
- A169πm
2 - B172πm
2 - C165πm
2 - D180πm
2
Solution & Step-by-step Explanation
Let the radius of the cone be r, height be h, and slant height be l.
Given:
Slant height (l) = 15m
Height (h) = 9m
Using the Pythagorean relation for a cone (l
2
=r
2
+h
2
):
15
2
=r
2
+9
2
225=r
2
+81
r
2
=225−81=144
r=
144
=12m
The formula for the Curved Surface Area (CSA) of a cone is:
CSA=πrl
Substituting the values:
CSA=π×12×15=180πm
2
Given:
Slant height (l) = 15m
Height (h) = 9m
Using the Pythagorean relation for a cone (l
2
=r
2
+h
2
):
15
2
=r
2
+9
2
225=r
2
+81
r
2
=225−81=144
r=
144
=12m
The formula for the Curved Surface Area (CSA) of a cone is:
CSA=πrl
Substituting the values:
CSA=π×12×15=180πm
2