A swimming pool is 12 m long, 6 m wide, 1 m deep at the...

Name: A swimming pool is 12 m long, 6 m wide, 1 m deep at the shallow end, and 3 m deep at the deep end, as shown in the figure. Water is being pumped into the pool at 0.25 m³/minute. Find the rate of rise of the water level of the swimming pool at the moment when there is 1 m of water at the deep end.
Uploaded: 2022-12-17T07:11:10-08:00
Duration: 4 min 54 s
Channel: Brent Burkett
Description: A swimming pool is 12 m long, 6 m wide, 1 m deep at the shallow end, and 3 m deep at the deep end, as shown in the figure. Water is being pumped into the pool at 0.25 m³/minute. Find the rate of rise of the water level of the swimming pool at the moment when there is 1 m of water at the deep end.

A swimming pool is 12 m long, 6 m wide, 1 m deep at the shallow end, and 3 m deep at the deep end, as shown in the figure. Water is being pumped into the pool at 0.25 m³/minute. Find the rate of rise of the water level of the swimming pool at the moment when there is 1 m of water at the deep end.

Transcript

0:00 All right.

00:01 So this third time i'm doing this problem.

00:02 It kept shutting out on me on the whiteboard.

00:04 I guess they just want me to do a quick answer, not really explain anything.

00:09 It's a $2 .50.

00:10 Frican question.

00:12 It's a cow question.

00:14 All right.

00:15 Anyway, enough of my rant.

00:17 Here's what we got.

00:18 We want to find out how high this pool or how fast the height of this water is changing.

00:23 We have a little tiny triangle right here.

00:27 Okay.

00:29 There's a certain height.

00:34 H, we don't know how wide it is.

00:36 Now, we can find the volume of this thing by, by, you know, finding the volume of this is going to be the area of the triangle times of the six meters that this goes back.

00:59 Now, if we go all the way to the end of the pool, and that's kind of the important thing, if we go up a certain height and all the way over here, this is now 12 meters.

01:13 All right.

01:14 Now, since we're assuming the top of the pool is the same on both sides.

01:21 So on the left side, it goes down three feet.

01:23 On the right side, it only goes down one feet.

01:25 So we're assuming that this, or meters, this is two meters.

01:30 So we have this red triangle.

01:32 That's if we go all the way to the end of the pool and get our triangle that way.

01:38 And this is going to be two meters.

01:40 So what that means is two times six gives us 12.

01:43 So that means there's a the short side is one six the longer side.

01:49 We need that because in our as the water rises, this this side of it is going to be 6h...