Question

rowan is taking his siblings to get ice cream. they cant decide whether to get a cone or a cup because they want to get the most ice cream for their money. if w = 2.5 in, x = 5 in, y = 5 in, z = 3 in, and the cone and cup are filled evenly to the top with no overlap, which container will hold the most ice cream? use 3.14 for π, and round your answer to the nearest tenth.

Explanation:

Step1: Recall volume formulas

The volume formula for a cone is $V_{cone}=\frac{1}{3}\pi r^{2}h$, where $r = w$ and $h=x$. The volume formula for a cylinder is $V_{cylinder}=\pi r^{2}h$, where $r = \frac{y}{2}$ and $h = z$.

Step2: Calculate volume of the cone

Substitute $w = 2.5$ in, $x = 5$ in and $\pi=3.14$ into the cone - volume formula.
$V_{cone}=\frac{1}{3}\times3.14\times(2.5)^{2}\times5=\frac{1}{3}\times3.14\times6.25\times5=\frac{3.14\times31.25}{3}\approx32.7$ in³.

Step3: Calculate volume of the cylinder

First, the radius of the cylinder $r=\frac{y}{2}=\frac{5}{2}=2.5$ in, and $h = z = 3$ in.
Substitute into the cylinder - volume formula: $V_{cylinder}=3.14\times(2.5)^{2}\times3=3.14\times6.25\times3 = 58.9$ in³.

Answer:

The cylinder will hold the most ice - cream. The volume of the cone is approximately $32.7$ in³ and the volume of the cylinder is approximately $58.9$ in³.