A triangular tank measuring 8m tall, 3m long, and 2m across...

Name: A triangular tank measuring 8m tall, 3m long, and 2m across contains water m deep. Which of the following integrals represents the work required to pump all the water out of the top of the tank? (Assume the acceleration due to gravity is 10 m/s² and the density of water is 1000 kg/m³ )
Uploaded: 2022-08-08T00:42:47-08:00
Duration: 6 min 2 s
Channel: Eduard Sanchez
Description: A triangular tank measuring 8m tall, 3m long, and 2m across contains water m deep. Which of the following integrals represents the work required to pump all the water out of the top of the tank? (Assume the acceleration due to gravity is 10 m/s² and the density of water is 1000 kg/m³ )

A triangular tank measuring 8m tall, 3m long, and 2m across contains water m deep. Which of the following integrals represents the work required to pump all the water out of the top of the tank? (Assume the acceleration due to gravity is 10 m/s² and the density of water is 1000 kg/m³ )

Transcript

0:00 Hi there.

00:01 So for this problem, we are told that an aquarium is six meters long, one meter wide, and one meter deep, and it's full of water.

00:26 So we need to find the word needed to pump half of the water out of the aquarium.

00:34 And yes, we need to use the fact that the density of water is 1 ,000 kilograms per cubic meter.

00:42 So for part a, we need to show how to approximate the required word by a remand sum.

00:51 So let's say that that is part a of this problem.

00:55 So let's start by setup the integral.

00:58 We divide the upper half of the aquarium into horizontal slides, and for each slice, let x denote its distance from the top of the tank, and delta x denotate its thickness.

01:12 So we choose horizontal slice because we want that each drop of this water in a given slice to be the same distance from the top of the tank.

01:24 Now, using the formula at the beginning that we know for the word done, a word of a slide is equal to the force d times the distance d.

01:36 Now, remember that we can write the force as the mass times the acceleration times, well, the distance d in this case.

01:45 Now, we can write the mass, remember that we can write the mass times the part between the density and the volume of the object, this times the acceleration, this times the distance d.

01:56 Now, since the length, width and thickness of the slides are given, which are 6 meter, 1 meter, and what we are going to call delta x, respectively, it's volume, we can write the volume as just 6 times 1 times delta x.

02:25 So that will be just simply 6 times delta x.

02:32 Does the equation from before for the word done, so we now can approximate that the word done is.

02:38 The density that we know we are given 1 ,000, this times 6 times delta x, which is the volume, times the gravity, which is 9 .8 meters per second square.

02:53 This times the distance adds that this is going to move.

02:59 Now we can simplify this as just the product between 1 ,000 times 9 .8 times 6.

03:10 So we obtain 58 ,800 times the distance x times delta x...

Question

A triangular tank measuring 8m tall, 3m long, and 2m across contains water m deep. Which of the following integrals represents the work required to pump all the water out of the top of the tank? (Assume the acceleration due to gravity is 10 m/s² and the density of water is 1000 kg/m³ )

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