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Probability

Question
CBSEENMA9003464
Wired Faculty App

The surface area of a sphere of radius 5 cm is 5 times the area of the curved surface of a cone of radius 4 cm. Find the height of the cone.

Solution

Surface area of sphere of radius 5 cm = 4π (5)2 cm2
Area of the curved surface of cone of radius 4 cm = π(4) l cm2 where I cm is the slant height of the cone.
According to the question,
4straight pi(5)2 = 5[straight pi(4)l}
rightwards double arrow     l = 5 cm
rightwards double arrow space space space space space space space space space square root of straight r squared plus straight h squared end root space equals space 5
rightwards double arrow        r2 + h2 = 25  rightwards double arrow   (4)2 + h2 = 25
rightwards double arrow       16 + h2 + 25  rightwards double arrow    h2 = 9
rightwards double arrow       h = 3
Hence, the height of the cone is 3 cm.

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