



 
Hi Tim, I drew your cup (not to scale) and then extended it downwards to form a cone. The dimensions are in inches. Triangles $ABC$ and $EDC$ are similar and hence \[\frac{3}{10 + b} = \frac{1}{b}.\] Solving for $b$ gives $b = 5$ inches. Now suppose that the water has been flowing into the cup for a while and the height of the water is $h(t)$ inches and the radius of the top of the water is $r(t)$ inches. $t$ is time in minutes. The volume of a cone of radius $r$ inches and height $h$ inches is $\frac13 \pi r^2 h$ cubic inches and hence, since $b = 5$ the volume of water in your cup $t$ minutes after the water begins to pour in is \[V(t) = \frac13 \pi \; r(t)^2 (h(t) + 5)  \frac13 \pi \;1^2 5.\] Can you complete the problem from here? Write back if you need more assistance. Penny  


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