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2021 AMC 10A Problems/Problem 17

Revision as of 22:01, 11 February 2021 by Cooljupiter (talk | contribs) (→‎Video Solution by pi_is_3.14 (using Vandermonde's Identity))

Two right circular cones with their vertex faced down are filled with the same amount of liquid, and the radii of the top of the liquids are $3\text{cm}$ and $6\text{cm}$ respectively. A spherical marble of radius $1\text{cm}$ is submerged into the liquids of both cones. What is the ratio of the rise of the liquid level in the narrow cone to the rise of the liquid level in the wide cone?

$\textbf{(A) } 1:1\qquad\textbf{(B) } 47:43\qquad\textbf{(C) } 2:1\qquad\textbf{(D) } 40:13\qquad\textbf{(E) } 4:1\qquad$

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