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the suface area of a sphere of radius 5cm is 5 times curved surface area of a cone of radius 4cm find the height and volume of the cone
Let R be the radius of the sphere.
Suppose the radius of cone be r and h respectively.
Surface area of the sphere = 4?R2 = 4? (5 cm)2
  =100? cm2
Curved surface area of cone = ?rl = ? × 4 cm × l                                        = 4?l

Given, Surface area of the sphere = 5 × Curved surface area of the cone
? 100? cm2 = 5 × 4? l cm
? 100? cm2 = 20?l cm
? l = 5 cm
Slant height of the cone,
? (4 cm)2 + h 2 = (5 cm)2
? h 2 = 25 cm2 – 16 cm2
? h 2 = 9 cm2
? h = 3 cm
Height of the cone, h = 3 cm
? Volume of the cone


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