Trouble with a hard question...

[takkamek_]

So as I've been doing some preparation questions before school starts, I've been stuck in this hard question.

"Scientists have built a ship that is 6 meters tall. The ships cross-section at the height y is a square, with a side length (m) is:


Specify the ships volume (m^3). "

So, like... Where do I start? I'm completely lost here. Since this is from a math book that focuses on integrals and derivatives, I assume I have to use them to solve this.

 

[tkhunny]

So as I've been doing some preparation questions before school starts, I've been stuck in this hard question.

"Scientists have built a ship that is 6 meters tall. The ships cross-section at the height y is a square, with a side length (m) is:

View attachment 9958
Specify the ships volume (m^3). "

So, like... Where do I start? I'm completely lost here. Since this is from a math book that focuses on integrals and derivatives, I assume I have to use them to solve this.

You probably should start with a good question. If the ship is 6m tall, then we're kind of done, since only y = 6 matters. Is there a picture to suggest that the ship is less than 6m in other spots besides the very middle?

 

[Dr.Peterson]

So as I've been doing some preparation questions before school starts, I've been stuck in this hard question.

"Scientists have built a ship that is 6 meters tall. The ships cross-section at the height y is a square, with a side length (m) is:

View attachment 9958
Specify the ships volume (m^3). "

So, like... Where do I start? I'm completely lost here. Since this is from a math book that focuses on integrals and derivatives, I assume I have to use them to solve this.

I presume what this means is that at any height y above the lowest point of the ship and below the highest point (6 meters), the horizontal cross-section is a square with the indicated side length. So you can find the area of any horizontal cross-section, and the volume will be the integral of that with respect to y. Do you follow that? If so, do it. If not, tell us more about what you don't get. Have you studied volumes by integration? How about areas? What have you learned about integrals?

 

[lev888]

This is a strange shape for a ship. Anyway, the horizontal cross-sections of the ship are squares. The side length of the square is described by the 3 functions (e.g. at the height of y=1.5m the side length is 5e^0.5*1.5). You need to lookup some area/volume formulas that use these functions. There will probably be integration involved at some point.