Question

an unopened can of iced tea contains 350 cubic centimeters of liquid. if the van is 5 inches long and has a .8 inch diameter, which is the best estimate of the volume of iced tea contained in the top 3 inches of the can

Answer 1

the can is 5 inches tall, so its height is 5 inches, so 3 inches off 5 inches that'd be 3/5.

the can has a diameter of 0.8 inches, meaning it has a radius of half that, or 0.4 inches.

if say the volume of iced-tea is V, how much is 3/5 of V? well, is just their product.

`\bf \textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=0.4\\ h=5 \end{cases}\implies V=\pi (0.4)^2(5)\implies V=0.8\pi \\\\\\ \stackrel{\textit{and 3/5 of that will be}}{\cfrac{3}{5}\cdot 0.8\pi }\implies V\approx \stackrel{in^3}{1.51}`