Answer:
Colin will have to wait for 2 hours for the pond to completely empty
Step-by-step explanation:
Volume of a Prism
The volume of a prism of base area Ab and height H is computed with the formula:
V=Ab.H
We are given a pond in the shape of a prism with a trapezoidal base (front view).
The area of a trapezoid of bases b1 and b2, and height a, is given by:
[tex]\displaystyle A_b=\frac{b_1+b_2}{2}.a[/tex]
The parallel bases of the trapezoid have measures of b1=0.6 m and b2=1.4 m, and the height is a=2 m, thus the area is:
[tex]\displaystyle A_b=\frac{0.6+1.4}{2}*2[/tex]
[tex]A_b=2\ m^2[/tex]
The height of the prism is H=1m, thus the volume of the pond is:
[tex]V=2\ m^2*1\ m[/tex]
[tex]V=2\ m^3[/tex]
It's also known the level of the pond goes down by 20 cm (0.2 m) in the first 30 minutes. Note at this moment the level is still at the rectangular prism zone of the pond, thus the volume of water is calculated as the area of the face of water by the height it went down:
[tex]V_w=1\ m*2\ m*0.2\ m = 0.4\ m^3[/tex]
The pond still has this volume of water:
[tex]V_p=2\ m^3-0.4\ m^3=1.6\ m^3[/tex]
The pond was drained [tex]0.4\ m^3[/tex] in 30 minutes, thus the rest of the water will be taken out in
[tex]\frac{1.6}{0.4}*30 =120\ min[/tex]
Thus, Colin will have to wait for 2 hours for the pond to completely empty
