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Question
A sphere has the same curved surface area as the curved surface area of a cone of height 36 cm and base radius 15 cm . Find the radius of the sphere .
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Solution
Radius of cone = 15 cm
Height of cone = 36 cm
Curved surface of the cone = `pirl`
`l = sqrt(r^2 + h^2) = sqrt(15^2 + 36^2) = sqrt(1521) = 36`
Curved surface of cone = `22/7 xx 15 xx 39 = 1838.571` cm2
Curved surface of cone = Curved surface of sphere
⇒ `4pir^2 = 1838.571`
⇒ `4 xx 22/7 xx r^2 = 1838.571`
⇒ `r^2 = (1838.571 xx 7)/(4 xx 22)`
⇒ `r^2 = 146.25`
⇒ r = 12.09 cm
The radius of the sphere = 12.09 cm
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