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Question
The area of the base of a right circular cone is 154 cm2 and its height is 14 cm. Its curved surface area is
Options
154`sqrt(5) "cm"^2`
`154 sqrt(7) "cm"^2`
`77sqrt(7) "cm"^2`
`77sqrt(5) "cm"^2`
Solution
`154 sqrt(5) "cm"^2`
Area of the base of the of a right circular cone = πr2
Therefore,
`=> 22/7xx"r"^2 = 154`
`=> "r"^2 = (154xx7/22)`
⇒ r2 = 49
⇒ r= 7 cm
Now, r = 7 cm and h = 14 cm
Then, slant height of the cone,`"l" = sqrt("r"^2 + "h"^2)`
`=sqrt((7)^2 + (14)^2)`
`=sqrt(49 + 196)`
`= sqrt(245)`
`= 7sqrt(5) "cm"`
Hence, the curved surface area of the cone = πrl
`= (22/7xx7xx7xxsqrt(5)) "cm"^2`
`=154 sqrt(5) "cm"^2`
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