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 = 3 in, x = 6 in, y = 6 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: Calculate volume of cone

The volume formula for a cone is $V_{cone}=\frac{1}{3}\pi r^{2}h$. Here, the radius $r = w=3$ in and height $h = x = 6$ in. Substitute the values: $V_{cone}=\frac{1}{3}\times3.14\times3^{2}\times6$. First, calculate $3^{2}=9$. Then, $\frac{1}{3}\times3.14\times9\times6 = 3.14\times3\times6= 56.52$ in³.

Step2: Calculate volume of cylinder

The volume formula for a cylinder is $V_{cylinder}=\pi r^{2}h$. Here, the radius $r = y/2 = 6/2=3$ in and height $h = z = 3$ in. Substitute the values: $V_{cylinder}=3.14\times3^{2}\times3$. Calculate $3^{2}=9$, then $3.14\times9\times3=84.78$ in³.

Step3: Compare volumes

Since $84.78>56.52$, the cylinder (cup) holds more ice - cream.

Answer:

The cup holds more ice - cream.