Answer: The slant height of the cone is 65.6 m
Step-by-step explanation:
Given: The diameter of a cone = 10 m
Surface area of cone = 190.6 m²
To find: Slant height
Diameter of cone = 10 m
Therefore Radius of cone = [tex]\dfrac{\text {Diameter }}{2} = \dfrac{10}{2} =5m[/tex]
As we know that surface area of a cone is given by
[tex]S.A. = \pi r(l+r)[/tex]
Where S.A. is surface area , r is the radius of cone and l is the slant height of the cone.
Let Slant height = l
So we have
[tex]190.6 = \dfrac{22}{7} \times 5 ( 5+l)\\\\\Rightarrow 5+l= \dfrac{190.6 \times 7}{22}\\\\\Rightarrow l= \dfrac{1334.2}{22}+5\approx 60.64+5 = 65.64\approx65.6[/tex]
Hence the slant height of the cone is 65.6 m
