Q8 of 56 Page 13

A cone of height 20 cm and radius of base 5 cm is made up of modeling clay. A child reshapes it in the form of a sphere. Find the diameter of the sphere. (CBSE 2011)

  1. Radius of the cone = r = 5 cm

Height of the cone = h = 20 cm


Let R be the radius of the sphere.


Since Volume of a solid remains unchanged if transformed from one shape to other.


∴ Volume of cone = Volume of sphere


πr2h = πR3


⇒ r2h = 4R3


⇒ (25 × 20)/4 = R3


⇒ R3 = 125


⇒ R = 5


∴ R = 5 cm.


Thus, diameter of the sphere = 5 × 2 = 10 cm.

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