This is a pond in the shape of a prism. It is completely full of water
Colin uses a pump to empty the pond.
The level goes down by 30 cm in the first 30 minutes.
Work out how many minutes Colin has to wait for
the pond to completely empty.
Answers
Kindly check picture to the question below.
Answer:
150 minutes
Step-by-step explanation:
Volume of prism = height * base area
Height of prism = 1m
Base area = area of a trapezium
Area of trapezium = 0.5(a + b) h
a, b = parallel sides, h= height of trapezium
Area of trapezium = 0.5(1.4+0.6)*2
Area = 0.5(2)*2 = 2m²
Hence,
V of prism = area of trapezium * height of prism
Volume = 2m² * 1m = 2m³
Decrease in water level due to pumping
20cm decrease in 30minutes
(20/100)m in 30 minutes
0.2 m decrease in height of water
Hence, height of water in prism after 30 minutes pumping :
height - 0.2 = 1 - 0.2 = 0.8m
Volume after 30 minutes of pumping :
Base area * new height
2m² * 0.8m = 1.6m³
Decrease in volume over 30 minutes :
(Initial volume - volume after pumping)
2m³ - 1.6m³ = 0.4m³
If ;
0.4m³ = 30 minutes
1.6m³ = x
0.4x = 48
x = 48 / 0.4
x = 120
Hence, it takes 120 minutes for the remaining 1.6m³ to be emptied.
Hence, total wait time :
120 minutes + 30 minutes
= 150 minutes
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