Question

A rectangular water reservoir contains 105 m³ of water. Find the depth of the water in the reservoir if its base measures 12 m by 3.5 m.

Answer 1

$$\begin{gathered} \mathrm{Length}\mathrm{of}\mathrm{the}\mathrm{rectangular}\mathrm{water}\mathrm{reservoir}=12\mathrm{m} \\ \mathrm{Breadth}=3.5\mathrm{m} \\ \mathrm{Suppose}\mathrm{that}\mathrm{the}\mathrm{height}\mathrm{of}\mathrm{the}\mathrm{reservoir}=h\mathrm{m} \\ \mathrm{Also},\mathrm{it}\mathrm{contains}105{\mathrm{m}}^3\mathrm{of}\mathrm{water},\mathrm{i}.\mathrm{e}.,\mathrm{its}\mathrm{volume}=105{\mathrm{m}}^3 \\ \mathrm{Volume}\mathrm{of}\mathrm{the}\mathrm{cuboidal}\mathrm{water}\mathrm{reservoir}=\mathrm{length}\times \mathrm{breadth}\times \mathrm{height} \\ \Rightarrow 105=12\times 3.5\times h \\ \Rightarrow 105=42\times h \\ \Rightarrow h=\frac{105}{42}=2.5\mathrm{m} \\ \therefore \mathrm{The}\mathrm{depth}\mathrm{of}\mathrm{the}\mathrm{water}\mathrm{in}\mathrm{the}\mathrm{reservoir}\mathrm{is}2.5\mathrm{m}. \end{gathered}$$