TV transmitter

The volume of water in a rectangular swimming pool is 6,998.4 hectolitres. A promotional leaflet states that if all the pool water were to fill a regular quadrilateral prism with a base edge equal to the average depth of the pool, the prism would have to be as tall as a nearby TV transmitter. Furthermore, to swim a distance equal to the transmitter's height, one would have to swim either eight lengths or fifteen widths of the pool. How tall is the TV transmitter?

Final Answer:

x =  216 m

Step-by-step explanation:

$$\begin{gathered} V=6998.4\text{hl}\to {\text{m}}^3=6998.4:10{\text{m}}^3=699.84{\text{m}}^3 \\ V=abc \\ V=c^{2}x \\ x=8a \\ x=15b \\ c{x}^2/120=V \\ c(V/c^2{)}^2/120=V \\ c=\sqrt[3]{699.84/120}=\frac{9}{5}=1.8\text{m} \\ x=V/c^2=699.84/1.8^2=216=216\text{m} \\ \text{ Verifying Solution: } \\ a=x/8=216/8=27\text{m} \\ b=x/15=216/15=\frac{72}{5}=14.4\text{m} \\ {V}_2=a\cdot b\cdot c=27\cdot 14.4\cdot 1.8=\frac{17496}{25}=699.84{\text{m}}^3 \end{gathered}$$

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