Question

According to the Polar Science Center, the arctic sea ice volume fluctuates between April and September every year. Next year the arctic sea volume is expected to be 28,000 cubic km in April and 11,500 cubic km in September. The area the ice covers is typically reduced by 30% between April and September. For example, if the area of the ice extent was 1000 square kilometers in April, then the area of the ice extent would be 700 square kilometers in September.

(1) Determine how much the thickness (height) of the ice will change by next year? (20%, 30%, 40%, 50%?)

Answer 1

Let us consider

April Area =A1, Height=H1

September   Area =A2, Height=H2

the arctic sea volume is expected to be 28,000 cubic km in April and 11,500 cubic km in September is given

it means A1*H1= 28000 ................(1)

A2* H2= 11500.......................(2)

A2/ A1= 0.7 is given by

Dividing two equations (1) and (2)

A1 * H1 / A2 * H2= 28000/11500

H1/H2= (28000/11500)*A2/ A1

H1 /H2 = (28000/11500)* 0.7

H1/H2=(2.434)*0.7

H1/H2= 1.703

H2/H1=1/1.703

H2/H1= 0.588

area of the ice extent was 1000 square kilometers

so it means

1-0.58=0.42

Thickness of ice will reduce by 42%

rounding of this percentage approximately 40% reduction in thickness

so option is "C".