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A conical flask is full of water. The flask has base radius a and height 2a. The water is poured into a cylindrical flask of base-radius $2 a 3$ . Find the height of water in the cylindrical flask.

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52 a

2 a

32 a

1 a

answer is C.

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Detailed Solution

Volume of a cone is

13 π r 2 h

,
Volume of a cylinder is

π r 2 h

,
We are given that the conical flask has base radius a and height 2a and the cylindrical flask has base-radius

2 a 3

.
We have to find the height of water in the cylindrical flask.

Volume of the conical flask is

13 π r 2 h

⇒ V o l u m e c o n e = 13 π r 2 h ​ r = a, h = 2 a, π = 227 ​ ⇒ V o l u m e c o n e = 13 × 227 × a 2 × 2 a = 4421 a 3 c u b e . u n i t s ​

Volume of a cylindrical flask is

π r 2 h

⇒ V o l u m e c y l i n d e r = π r 2 h ​ r = 2 a 3, h = ?, π = 227 ​ ⇒ V o l u m e c y l i n d e r = 227 × 2 a 3 2 × h ​ ⇒ V o l u m e c y l i n d e r = 227 × 4 a 2 9 h = 88 a 2 h 63 c u b e . u n i t s ​

Volume of the conical flask = Volume of the cylindrical flask

⇒ V o l u m e c o n e = V o l u m e c y l i n d e r ​ ⇒ 4421 a 3 = 88 a 2 h 63 ​ ⇒ h = 4421 a 3 × 63 88 a 2 ​ ⇒ h = a 3 a 2 × 4421 × 6388 ​ ∴ h = 32 a ​

Therefore the height of the water in the flask is

32 a

units.
So, the correct answer is Option 3.

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