Difference between revisions of "2021 AMC 10A Problems/Problem 17"
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| − | + | 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 <math>3\text{cm}</math> and <math>6\text{cm}</math> respectively. A spherical marble of radius <math>1\text{cm}</math> 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? | |
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| + | <math>\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</math> | ||
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| + | ==Video Solution by Hawk Math== | ||
| + | https://www.youtube.com/watch?v=AjQARBvdZ20 | ||
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| + | ==Video Solution by pi_is_3.14 (using Vandermonde's Identity)== | ||
| + | https://www.youtube.com/watch?v=mki7xtZLk1I | ||
| + | |||
| + | ~pi_is_3.14 | ||
Revision as of 22:58, 11 February 2021
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 
and 
respectively. A spherical marble of radius 
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?
Video Solution by Hawk Math
https://www.youtube.com/watch?v=AjQARBvdZ20
Video Solution by pi_is_3.14 (using Vandermonde's Identity)
https://www.youtube.com/watch?v=mki7xtZLk1I
~pi_is_3.14
