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A solid right circular cone of height 120 cm and radius 60 cm is placed in a right circular cylinder full of water of height 180 cm such that it touches the bottom. What will be the volume of water left in the cylinder, if the radius of the cylinder is equal to the radius of the cone?

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1.584 m 3

1.594 m³

1.603 m³

1.308 m³

answer is A.

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Detailed Solution

Given that the height of circular cone =120 cm and radius is 60 cm
And level of water filled in circular cylindrical h= 180 cm.
Determining the volume of the cylinder:

V 1 = π R 2 H V 1 = 227 × 602 × 180 V 1 = 2036571.429 c m 3

Also, volume of the cone:

V 2 = 13 π r 2 h V 2 = 13 × 227 × 602 × 120 V 2 = 452571.4286 c m 3

Now determining the volume of water left after immersing the cone into cylinder full of water:

V = V 1 − V 2 V = 2036571.429 − 452571.4286 V = 1584000 c m 3 V = 1.584 m 3

Therefore, 1 is the correct answer.

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