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The height of a glass tumbler is 12 cm. The radius of its circular base is 3 cm and that of its rim is 4 cm. The volume of the tumbler is :

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473.82 ml

464.95 ml

454.76 ml

459.86 ml

answer is B.

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Detailed Solution

In triangle COA and CPB.

$\frac{C O}{C B} = \frac{O A}{P B} = \frac{4}{3} \Rightarrow 3 C O = 4 C B \Rightarrow 3 C B + 3 \times 12 = 4 C B \Rightarrow C B = 36$

The volume of the glass tumbler

$= \frac{1}{3} π (4^{2} \times 48 - 3^{2} \times 36) = 464.95 mL$

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