Basic Calculus volume question

In summary, the conversation discusses finding the water height in a half cylinder water tank with a radius of 10 feet and a side length of 30 feet in order for the tank to be half full. The volume of the tank is calculated using the volume of a cylinder formula, and the conversation also mentions using an integral to solve the problem. The correct answer is determined to be 7.7, although there may be some formatting inconsistencies in the conversation.
  • #1
bopll
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Homework Statement



A water tank is in the shape of a half cylinder sitting on its side (not its top or its bottom). Let the radius be 10 ft and let the side-lenth on the floor be 30 feet. What should be the water height, measured from the floor up, so that the water tank is half full?

Homework Equations



Volume of a cylinder- h*(pi)r^2

The Attempt at a Solution



First i found the volume needed, which is (30)*(10)^2*pi/2 = 4712.4

Then I tried this problem breaking down rectangular boxes into dy components and set up the integral as follows (using 2sqrt(100-y^2 as the width of the boxes and y as the height of the boxes and 30 being the constant length)

30[tex]\int^{0}_{h}[/tex][tex]\2sqrt{100-y^{2}}[/tex]*2y dy

and set it equal to the needed volume.

I ended up getting 7.7, which i feel is wrong because the height should be less than half of the radius by just thinking about what SHOULD happen.

Should i be taking an entirely different approach to this or what?

ps sorry for the formatting inconsistencies... kinda new here.

thanks guys.

edit: i can't get my bounds right for whatever reason, but i set it from 0 to h.
 
Last edited:
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  • #2
nevermind, i guess i did the calculations wrong.

Can anyone confirm this setup at least?
 

What is the formula for finding the volume of a solid using basic calculus?

The formula for finding the volume of a solid using basic calculus is V = ∫a^b A(x)dx, where a and b are the limits of integration and A(x) is the cross-sectional area of the solid at a given point x.

What is the difference between basic calculus and advanced calculus when it comes to finding volume?

The main difference between basic calculus and advanced calculus when it comes to finding volume is the complexity of the shapes that can be calculated. Basic calculus is limited to simple shapes such as cylinders, cones, and spheres, while advanced calculus allows for the calculation of more complex shapes such as ellipsoids and hyperboloids.

When should I use basic calculus to find the volume of a solid?

Basic calculus should be used to find the volume of a solid when the shape of the solid is simple and can be easily defined by a function. It is also useful when the limits of integration can be easily determined.

What are some common applications of using basic calculus to find volume?

Some common applications of using basic calculus to find volume include calculating the volume of a water tank, determining the amount of medication in a pill, and finding the volume of a cone-shaped ice cream cone.

What are some common mistakes to avoid when using basic calculus to find volume?

Some common mistakes to avoid when using basic calculus to find volume include using the wrong limits of integration, forgetting to include units in the final answer, and not properly understanding the shape of the solid being calculated.

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