A tea bag can be modeled by the following square with a base edge of s= 4 centimeters and a height of l= 5 centimeters.
Since AB is half the side length, AB=2 centimeters. Now, let's use the Pythagorean Theorem for right â–³ ABC to find the height of the pyramid h.
AB^2+AC^2=BC^2
2^2+ h^2= 5^2
4+h^2=25
h^2=21
sqrt(h^2)=sqrt(21)
h=sqrt(21)
Now, let's use the formula for the volume of a pyramid to find the volume of the tea bag, \textcolor{darkorange}{V_\text{tea bag}}.
\begin{gathered}
\textcolor{darkorange}{V_\text{tea bag}}=\dfrac{1}{3}\textcolor{darkviolet}{B}h
\end{gathered}
The variable B represents the area of the base. Since the base is a square with a side s=4, its area is B=4^2=16 square centimeters. Now, let's substitute the values into the formula for \textcolor{darkorange}{V_\text{tea bag}}.
\textcolor{darkorange}{V_\text{tea bag}}=\dfrac{1}{3}\textcolor{darkviolet}{B}h
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Substitute values and evaluate
\textcolor{darkorange}{V_\text{tea bag}}=\dfrac{1}{3}(\textcolor{darkviolet}{16})(\sqrt{21})
\textcolor{darkorange}{V_\text{tea bag}}=\dfrac{1}{3}\cdot 16\sqrt{21}
\textcolor{darkorange}{V_\text{tea bag}}=\dfrac{16\sqrt{21}}{3}
\textcolor{darkorange}{V_\text{tea bag}}=24.440403\ldots
\textcolor{darkorange}{V_\text{tea bag}}\approx \textcolor{darkorange}{24.4}
Therefore, the volume of the tea bag is about 24.4 square centimeters.
