Question

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 20cm in the first 30 minutes. Work out how many minutes Colin has to wait for the pond to completely empty.

Answer 1

Answer:

150 minutes

Step-by-step explanation:

Volume of prism = $\text{Area of base} \times height$

Since base is in the form of trapezium .

So, we will use the formula of area of trapezium.

Height of trapezium = 2 m

Parallel sides measures 0.6 m and 1.4 m

Area of trapezium = $\frac{1}{2} \times{\text{sum of parallel sides}} \times height$

                              = $\frac{1}{2} \times(0.6+1.4) \times 2$

                              = $2m ^2$          

So, area of base = 2 square m

Height of prism = 1 m

So, Volume of prism = $2\times1$        

                                  = $2m^3$      

Thus the volume of pond is 2 cubic meter.

Now, we are given that The level goes down by 20cm in the first 30 minutes.

100 cm = 1 m

20 cm = 2/100 = 0.2 m

So, The level goes down by 0.2 m in the first 30 minutes.            

Since the pond was completely filled .

So, the height of water = height of prism = 1 m

Now since The level goes down by 0.2 m.

So, the height of remaining water = 1-0.2=0.8 m

So, Volume of remaining water = $\text{Area of base} \times height$

                                                    = $2\times 0.8$

                                                    = $1.6 m^3$

Volume of water emptied = total volume - remaining volume

                                          = 2-1.6

                                          =0.4 cubic m

Since 0.4 cubic m was emptied in 30 minutes

So, 1 cubic m is emptied in minutes = $\frac{30}{0.4}$

So, 1.6 cubic m is emptied in minutes = $\frac{30}{0.4}\times 1.6$

                                                              = $120$

Hence it will take 120 minutes to remove the remaining water

So, total time taken to empty the pond completely = 120+30=150 minutes.

Hence Colin has to wait for 150 minutes for the pond to completely empty.

Answer 2

Volume of the prism is given by:
V=(base area)*(height)
thus:
base area=1/2(a+b)*h
=1/2(1.4+0.6)*2
=2 m²

Thus the volume will be:
V=2*1
V=2 m³

Volume after 30 min:
V=2×(0.8)
V=1.6 m³

Rate of emptying the tank is:
(2-1.6)/30=1/ 75 m³/min
time taken to empty the tank:
time=volume/rate
time=2/(1/75)
=150 min