2/6/24, 1:43 PM
HW 3.3 Rates-Maria Huerta
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Student: Maria Huerta
Date: 02/06/24
Instructor: Dania Sinibaldi
Course: Quantitative Reasoning O06B SP24
Assignment: HW 3.3 Rates
A lake in a certain country has a volume of approximately cubic kilometers, and its surface area is square kilometers. Complete parts (a) through (c) below.
1950
67,555
a. What is the average depth of the lake (the depth of a box with the volume and surface area of the lake)?
With the volume and surface area known, there is one term that has units in cubic kilometers and one term that has units in square kilometers. A mathematical operation needs to be performed so that the resulting unit is kilometers. To find the average depth of the lake, divide by .
1950 km
3
67,555 km
2
Divide, rounding to three decimal places.
1950 km
3
67,555 km
2
=
1950 km
3
1
67,555 km
2
=
km
0.029
b. In the past six years, the water level of the lake has dropped feet from the depth computed in part (a). Approximately how much water has the lake lost?
6
To compute how much water the lake has lost in the past six years, the current volume must be compared to the previous volume. It is known that the previous volume was . The current volume must now be determined.
1950 kilometers
3
If , then feet is equal to kilometers.
1 ft = .0003048 km
6
6 ft
0.0003048 km
ft
Perform the multiplication, rounding to six decimal places.
6 ft
0.0003048 km
ft
=
6 ft
0.0003048 km
ft
=
km
0.001829
Therefore, there was a drop of kilometers. The loss of volume of water can be determined by .
0.001829
(0.001829 km)
67,555 km
2
Perform the multiplication, rounding to the nearest whole number.
(0.001829 km)
67,555 km
2
=
(0.001829 km)
67,555 km
2
=
km
124
3
Therefore, the lake lost km
of water.
124
3
c. What percentage of the volume (
) has been lost?
1950 kilometers
3
When calculating percentages, one term must be divided into another term.
Therefore, the percentage of volume that has been lost is , rounding to two decimal places.
124
1950
= 0.06
Therefore, the percentage of volume that has been lost is , or %.
0.06
6
