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Question

A hollow spherical ball whose inner radius is 4 cm is full of water. Half of the water is transferred to a conical cup and it completely filled the cup. If the height of the cup is 2 cm, then the radius of the base of cone, in cm is:
  1. 4cm
  2. 8πcm
  3. 8cm
  4. 16cm

A
4cm
B
8πcm
C
16cm
D
8cm
Solution
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The correct option is C 8cm
As half of the water in the spherical cup is transferred to the conical cup, half of the volume of water in the spherical cup is equal to the volume of water in the conical cup up to 2cm.

Volume of a cone =13πr2h where r is the radius of the base of the cone and h is the height.

Volume of a sphere of radius r =43πr3

Hence, 12× (Volume of sphere) = Volume of the cone

12×43π×43=13πr2×2

r2=64

r=8cm

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