KVPY SA Exam 2011 Question Paper

Question : 63 of 80

Marks: +1, -0

The diameter of one of the bases of a truncated cone is 100 mm. If the diameter of this base is increased by 21% such that it still remains a truncated cone with the height and the other base unchanged, the volume also increases by 21%. The radius of the other base (in mm) is

Validate

Solution:

Let initially 2 bases have radii 5 cm and r cm.
Finally base have radii (1.21 × 5) and r
Ratios of volumes

=\V_2/\V_1=1.21

\V_2={πh}/3[(6.05)^2+(6.05)r+r^2]

\V_1={πh}/3[5^2+5r+r^2]

\V_2/\V_1=1.21

⇒{(6.05)^2+(6.05)r+r^2}/{5^2+5r+r^2}=1.21

⇒r^2=6.3525/21

⇒ r=11/2\cm=55\mm

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