Finding the volume of a cylinder

In summary, the conversation discusses an equation for a circle with a radius of 4 units and the attempt to find its volume when rotated about the y-axis. The correct formula for the volume of a sphere is given as pi*256/3, with no need for integration or breaking the integral into two parts. The equation x^2+y^2=16 is confirmed to be for a circle and not a cylinder.
  • #1
Geekchick
77
0

Homework Statement



x2+y2+16

Homework Equations



[tex]\pi[/tex][tex]\int^{b}_{a}[/tex]{R(x)2}dx

The Attempt at a Solution



I just need to know if i set this up right.

When I solve for y and graph it I get a semi circle that goes from -4 to 4.

[tex]\pi\int^{0}_{-4}[/tex]{([tex]\sqrt{(16-x^{2})}[/tex])[tex]^{2}[/tex]}dx + [tex]\pi\int^{4}_{0}[/tex]{([tex]\sqrt{(16-x^{2})}[/tex])[tex]^{2}[/tex]}dx

I get 85.4[tex]\pi[/tex]
 
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  • #2
You have given an expression but i'll assume you mean the equation for:

[itex] x^2 + y^2 - 16 = 0[/itex]

which is a circle whose centre is at 0,0 and has a radius of 4 units?

The area of such a cylinder would be

[itex] 16\pi l [/itex]

where l is the length of the cylinder.

I don't think you need to use [itex] \int_a^b y^2 dx [/itex] because you know the radius and it's not a volume of revolution.

If you want to find the sphere when the shape is rotated about the y-axis pi radians you can just use the formula

[itex] \frac{4}{3} \pi r^3 [/itex]

[itex] \frac{256}{3} \pi [/itex]

[itex] 85.3 \pi [/itex]

So no need for integration, but you got the right answer.
 
  • #3
It looks to me like you are trying to find the volume of a SPHERE by rotating a semicircle. So yes, the answer is correct. But no need to round it off or to break the integral into two parts. Like Gregg said it's pi*256/3. And the equation is x^2+y^2=16. This has nothing to do with cylinders.
 

Related to Finding the volume of a cylinder

1. How do you find the volume of a cylinder?

To find the volume of a cylinder, you need to use the formula V = πr²h, where r is the radius of the base and h is the height of the cylinder.

2. What is the unit for volume?

The unit for volume is typically expressed in cubic units, such as cubic centimeters (cm³) or cubic meters (m³).

3. Can you use the same formula to find the volume of any cylinder?

Yes, the formula V = πr²h can be used to find the volume of any cylinder, regardless of its size or shape.

4. How do you measure the radius and height of a cylinder?

The radius of a cylinder is the distance from the center of the circular base to the edge of the base. The height of a cylinder is the distance between the two circular bases. These measurements can be taken with a ruler or measuring tape.

5. Can you find the volume of a cylinder if the height is not given?

No, the height is a necessary component in the formula for finding the volume of a cylinder. If the height is not given, the volume cannot be accurately calculated.

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