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Question
If the area of the base of a right circular cone is 3850 cm2 and its height is 84 cm, then find the slant height of the cone.
Solution
We have,
Height = 84 cm
Let the radius and the slant height of the cone be r and l, respectively.
Area of the base of the cone = 3850 cm2
`=> pi"r"^2 = 3850`
`=> 22/7xx"r"^2 = 3850`
`=> "r"^2 = 3850xx7/22`
`=> "r"^2 = 1225`
`=> "r" = sqrt(1225)`
∴ r = 35 cm
Now,
`"l" =sqrt("h"^2+"r"^2)`
`=sqrt(84^2+35^2)`
`=sqrt(7056+1225)`
`=sqrt(8281)`
= 91 cm
So, the slant height of the given cone is 91 cm.
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