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

Question

2 years ago

14

by 30 cm in the first 30 mins.
THE NUMBERS ARE DIFFERENT TO SIMILAR QUESTIONS

1 answer:

lapo4ka [179] · Answer 1 · 2024-01-03T21:55:23+03:00

The required time is mathematically given as

t-150 minutes.

This is further explained below.

We know that the volume of the prism is given by.

Volume $$=$ (Base Area $) \times$ Height$

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

Base Area $=2 \mathrm{~m}^2$

Now,

$Volume $=2 \times 1=2 \mathrm{~m}^3$$

Given that there is a twenty percent drop in the level of the pond during the first thirty minutes.

Because of this, the volume increases.

$Volume $=2 \times 0.8=1.6 \mathrm{~m}^3$

Now, the rate of emptying the tank is,

$=\frac{2-1.6}{30}=\frac{1}{75} \mathrm{~m}^3 / \mathrm{min}$

In conclusion, We also know that,

$$

$\begin{aligned}&\text { time }=\frac{\text { volume }}{\text { rate }} \\&\text { time }=\frac{2}{\frac{1}{75}}-150 \mathrm{~min}\end{aligned}$

Therefore, Colin must wait for the pond to drain for a total of 150 minutes.