Setting these integrals up is often the hardest part. Have you drawn a sketch of the solid?Math10 said:Homework Statement
Find the volume of the solid bounded by the cylinder y^2+z^2=9 and the planes x=0, y=0, z=0, and 2x+y=2.
Homework Equations
None.
The Attempt at a Solution
This is double integral problem. I know how to find the double integral but I don't know how to set it up. How do I find the limits of integration for this double integral?
Math10 said:Homework Statement
Find the volume of the solid bounded by the cylinder y^2+z^2=9 and the planes x=0, y=0, z=0, and 2x+y=2.
Homework Equations
None.
The Attempt at a Solution
This is double integral problem. I know how to find the double integral but I don't know how to set it up. How do I find the limits of integration for this double integral?
Neither of which is relevant to this problem.jedishrfu said:You need to setup the integral and then you'll know how to setup the limits.
There are some videos on the mathispower4u that talk about the washer method and the shell method:
x=0, y=0, z=0 isn't a plane, it is a point. I expect you mean the plane y=0, z=0.Math10 said:Find the volume of the solid bounded by the cylinder y^2+z^2=9 and the planes x=0, y=0, z=0, and 2x+y=2.
Svein said:x=0, y=0, z=0 isn't a plane, it is a point. I expect you mean the plane y=0, z=0.
Ah. Sorry.LCKurtz said:No, that is the three coordinate planes. He wrote what he meant there.
LCKurtz said:Neither of which is relevant to this problem.
The volume of a solid is the amount of space that it occupies in three-dimensional space. It is typically measured in units such as cubic meters or cubic feet.
The formula for finding the volume of a solid depends on its shape. For example, the volume of a cube can be found by multiplying the length of one side by itself three times (V = s^3). The volume of a cylinder can be found by multiplying the area of the base by the height (V= πr^2h).
The most commonly used units for volume are cubic meters (m^3) and cubic feet (ft^3). However, depending on the size of the solid, other units such as milliliters (mL) or gallons (gal) may be used.
Volume measures the space inside a solid, while surface area measures the outside surface of a solid. Volume is measured in cubic units, while surface area is measured in square units.
Yes, the volume of an irregularly shaped solid can be calculated by using the displacement method. This involves placing the solid in a container filled with water and measuring the change in water level. The change in water level is equal to the volume of the solid.