Mathematics: Which of the following best describes how the melted wax will fill the mold? TEKS G11(D) Adam has a spherical candle with a radius of 2 inches. He melts the candle completely and pours the soft wax into a mold in the shape of a rectangular prism. The dimensions of the mold are shown here. A B 2 in The wax will fill the mold a bit less than halfway The wax will fill the mold a bit more than halfway. The wax will fill the mold almost perfectly The wax will fill the mold and there will be a lot of

Which of the following best describes how the

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25.01.2022

The wax will fill the mold a bit more than halfway.

Step-by-step explanation:

The volume of a sphere with radius is:

$V = \displaystyle \frac{4}{3}\pi\, r^3$ .

The radius of this sphere of wax is $2\;\rm in$ ; Its volume would be:

$V(\text{sphere}) = \displaystyle \frac{4}{3}\pi \, r^3 = \frac{4}{3}\pi\times (2\; \rm in)^3 \approx 33.5\; \rm in^3$ .

Assume that the wax here does not evaporate, combust, or otherwise disappear. $V(\text{wax}) = V(\text{sphere}) \approx 33.5\; \rm in^3$ .

The volume of a rectangular prism is equal to $\text{Width} \times \text{Depth}\times \text{Height}$ .

For this mold with a rectangular prism shape:

$V(\text{mold}) = (2\; \rm in) \times (5\; \rm in) \times (5\; \rm in) = 50\; \rm in^3$ .

Half of that would be:

$\displaystyle \frac{1}{2}\,V(\text{mold}) = \frac{1}{2}\times 50\; \rm in^3 = 25\; \rm in^3$ .

Compare these two volumes to the volume of wax available:

$\displaystyle \frac{1}{2}\, V(\text{mold}) < V(\text{wax}) < V(\text{mold})$ .

In other words, the wax will fill the mold a bit more than halfway, but not completely.

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