Question

The kilopascal is a unit of measure for atmospheric pressure. Suppose the atmospheric air pressure at sea level is about 103 kilopascals. For every 1000-meter increase in altitude, the pressure decreases about 11.4%. What is the approximate pressure at an altitude of 3000 meters?

A. 75.06 kPa
B. 89.38 kPa
C. 96.24 kPa
D. 105.56 kPa

Answer 1

The atmospheric pressure at sea level is 103 kPa, and for each 1000-meter increase in altitude, it decreases by about 11.4%. By applying this percentage decrease step by step over a 3000-meter ascent, the approximate pressure at that altitude is calculated to be 71.638 kPa.

Step-by-step explanation:

The question asks to calculate the approximate atmospheric pressure at an altitude of 3000 meters, given that at sea level the pressure is about 103 kilopascals and it decreases by about 11.4% for every 1000-meter increase in altitude. To find the pressure at 3000 meters, we can apply the percentage decrease three times (once for each 1000 meters).

The pressure after the first 1000 meters: 103 kPa - (11.4% of 103 kPa) = 103 kPa - 11.742 kPa = 91.258 kPa

The pressure after the second 1000 meters: 91.258 kPa - (11.4% of 91.258 kPa) = 91.258 kPa - 10.403 kPa = 80.855 kPa

The pressure after the third 1000 meters: 80.855 kPa - (11.4% of 80.855 kPa) = 80.855 kPa - 9.217 kPa = 71.638 kPa

Therefore, the approximate pressure at an altitude of 3000 meters is 71.638 kPa, which is closest to option A, 75.06 kPa.