KVPY SA Exam 2015 Question Paper

Question : 64 of 80

Marks: +1, -0

Given are three cylindrical buckets X , Y,Z whose circular bases are of radii 1,2,3 units, respectively. Initially water is filled in these buckets upto the same height. Some water is then transferred from Z to X so that they both have the same volume of water. Some water is then transferred between X and Y so that they both have the same volume of water. If

h_Y,h_Z

denote the heights of water at this stage in the buckets Y,Z, respectively, then the ratio

h_Y/h_Z

equals

$4/9$
1
$9/4$
$81 / 40$

Validate

Solution:

Initially

V_1 = πH; V_2 = 4πH; V_3 = 9πH

Step-1 :

V_1 = 5πH; V_2 = 4πH; V_3 = 5πH

Step-2 :

V_1= 4.5 πH; V_2= 4.5 πH; V_3= 5πH

Hence

π2^ 2 .h_y = 4.5 πH

π3^ 2 h_z = 5 πH

⇒

{4h_y}/{9h_z}=4.5/5⇒ {4h_y}/{9h_z}= 81/40

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