Area under curves: f(x) = 20 - 0.024x^2 for -25 ≤ x ≤ 25

[yhpigs]

Hello everyone!

I have a revision question that I'm a little bit stuck on:



The roof of a stadium has the shape given by the function f(x) = 20 - 0.024x^2 for -25 [FONT=&quot]≤ [/FONT]x [FONT=&quot]≤ [/FONT]25

The stadium is 75m long and its cross-section is shown in the picture below:



Part a) asks to find the volume of the stadium.

I'm not quite sure where to start with this question, do I find the area under the curve and multiply it by 75 m?

 

[Harry_the_cat]

Hello everyone!

I have a revision question that I'm a little bit stuck on:



The roof of a stadium has the shape given by the function f(x) = 20 - 0.024x^2 for -25 ≤ x ≤ 25

The stadium is 75m long and its cross-section is shown in the picture below:

View attachment 10102

Part a) asks to find the volume of the stadium.

I'm not quite sure where to start with this question, do I find the area under the curve and multiply it by 75 m?

Yes, because the volume of a prism (which this is because it has a constant cross-section) is area of base x height. In this case the "base" is the cross-section and the "height" is the length.

 

[HallsofIvy]

Are you saying that the base of the stadium is a rectangular rather than circular?

 

[Dr.Peterson]

Hello everyone!

I have a revision question that I'm a little bit stuck on:



The roof of a stadium has the shape given by the function f(x) = 20 - 0.024x^2 for -25 ≤ x ≤ 25

The stadium is 75m long and its cross-section is shown in the picture below:

View attachment 10102

Part a) asks to find the volume of the stadium.

I'm not quite sure where to start with this question, do I find the area under the curve and multiply it by 75 m?

That's the easiest way. If you're learning to find volumes by double or triple integration, you can do that instead, but most of the work will be the same.

 

[Steven G]

Hello everyone!

I have a revision question that I'm a little bit stuck on:



The roof of a stadium has the shape given by the function f(x) = 20 - 0.024x^2 for -25 ≤ x ≤ 25

The stadium is 75m long and its cross-section is shown in the picture below:

View attachment 10102

Part a) asks to find the volume of the stadium.

I'm not quite sure where to start with this question, do I find the area under the curve and multiply it by 75 m?

This problem is as flawed as can be. You are told about the roof. The stadium can be a 5m X 5m X 5m cube with the roof as described on top of the cube. The stadium can also be 5m X 5m X 15m with the roof as described. Since you are not told what the shape is below the roof you can not answer that. After all, how many structures have you seen where the roof touches the floor?

 

[Dr.Peterson]

This problem is as flawed as can be. You are told about the roof. The stadium can be a 5m X 5m X 5m cube with the roof as described on top of the cube. The stadium can also be 5m X 5m X 15m with the roof as described. Since you are not told what the shape is below the roof you can not answer that. After all, how many structures have you seen where the roof touches the floor?

I don't see any problem; you seem to be missing several points.

The graph is said to be the cross-section of the stadium, and it (as well as the function definition) shows that the roof is 5 meters above ground at the ends (which are 50 meters apart). We are also told that the stadium is 75 meters long, which must be measured perpendicular to the cross-section, making the top view a rectangle. Who said the roof touches the floor, and what do you think the 75 refers to?

A few things could have been stated explicitly, but it's clear that none of your suggestions fit the data.

 

[Steven G]

I don't see any problem; you seem to be missing several points.

The graph is said to be the cross-section of the stadium, and it (as well as the function definition) shows that the roof is 5 meters above ground at the ends (which are 50 meters apart). We are also told that the stadium is 75 meters long, which must be measured perpendicular to the cross-section, making the top view a rectangle. Who said the roof touches the floor, and what do you think the 75 refers to?

A few things could have been stated explicitly, but it's clear that none of your suggestions fit the data.

You are correct that I missed a few details, especially looking at the image too quickly.

 

[mmm4444bot]

You are correct that I missed a few details, especially looking at the image too quickly.

That's what I did, too because as soon as I read "has the shape of" my gaze shifted to the quadratic to the image. I envisioned a volume of rotation. I noticed the 75, only after Halls posted a question.