Question

1. lake erie has an area of 2.6 x 10^4 km², and an average depth of 19.0 m. what is the volume of water in l. erie (hints: what is area?)?

Explanation:

Step1: Convert units

Convert the area from \(km^{2}\) to \(m^{2}\).
Since \(1\ km = 1000\ m\), then \(1\ km^{2}=(1000\ m)^{2}=10^{6}\ m^{2}\).
The area \(A = 2.6\times10^{4}\ km^{2}=2.6\times10^{4}\times10^{6}\ m^{2}=2.6\times 10^{10}\ m^{2}\).
The depth \(h = 19.0\ m\).

Step2: Calculate volume

The volume \(V\) of a body (assuming a simple shape where \(V = A\times h\), since area \(A\) is the base - area and \(h\) is the height or depth).
\(V=A\times h=(2.6\times 10^{10}\ m^{2})\times(19.0\ m)=4.94\times 10^{11}\ m^{3}\).

Step3: Convert volume to liters

Since \(1\ m^{3}=1000\ L = 10^{3}\ L\).
\(V=(4.94\times 10^{11}\ m^{3})\times(10^{3}\ L/m^{3}) = 4.94\times10^{14}\ L\).

Answer:

The volume of water in Lake Erie is \(4.94\times 10^{14}\ L\).