Determine the Volume of the solid ?

In summary, the problem is asking for the volume of a solid bounded by two surfaces, z=10-x^2 and z=y^2+1. To solve this, the intersecting points of the two surfaces were found, resulting in a circle with a center at (0,0) and a radius of 3. Using polar coordinates, the integral (9-x^2-y^2)drd@ was evaluated, with r going from 0 to 3 and theta going from 0 to 2*pi. It was then noted that the function should be multiplied by r in the integral.
  • #1
rclakmal
76
0

Homework Statement



determine the volume of the solid S which is bounded above by the surface z=10-x^2 and below by the z=Y^2+1;


Homework Equations





The Attempt at a Solution



what i did was first i tried to find the intersecting points of two surfaces .So i equal two functions and i got x^2+y^2=9 which is a circle center (0,0) and radius 3.then i used polar coordinates to evaluate this .

(r goes from 0 to 3 and theta goes from 0 to 2*pi )integrate (9-x^2-y^2)drd@.

am i correct ??or have i mad any kind of error?please explain?
 
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  • #2
rclakmal said:

Homework Statement



determine the volume of the solid S which is bounded above by the surface z=10-x^2 and below by the z=Y^2+1;


Homework Equations





The Attempt at a Solution



what i did was first i tried to find the intersecting points of two surfaces .So i equal two functions and i got x^2+y^2=9 which is a circle center (0,0) and radius 3.then i used polar coordinates to evaluate this .

(r goes from 0 to 3 and theta goes from 0 to 2*pi )integrate (9-x^2-y^2)drd@.

am i correct ??or have i mad any kind of error?please explain?

Usually you have the function (of course that needs to be in polar coordinates) not only with dr dtheta, but r dr dtheta, so from what you have done the integral is the function 9r - r^3 with respect to r and then theta. Someone should confirm that though since I haven't looked at this in a while.
 
  • #3
ah yr i forgot it thnaks !but am i right up to that point ?about setting the limits of the integral and other process ?
 

1. How do you determine the volume of a solid?

To determine the volume of a solid, you need to measure the length, width, and height of the solid and then use the formula V = lwh, where V is the volume, l is the length, w is the width, and h is the height.

2. Can the volume of a solid change?

Yes, the volume of a solid can change if the length, width, or height of the solid changes. For example, if you cut a cube in half, the volume of each half will be half of the original volume.

3. How is the volume of an irregularly shaped solid determined?

The volume of an irregularly shaped solid can be determined using the water displacement method. This involves submerging the solid in a container of water and measuring the volume of water displaced by the solid. The volume of the solid will be equal to the volume of water displaced.

4. What units are used to measure volume?

The most common units used to measure volume are cubic units, such as cubic centimeters (cm3) or cubic meters (m3). However, other units such as liters (L) or gallons (gal) can also be used.

5. How is the volume of a gas different from the volume of a solid?

The volume of a gas can change depending on its temperature and pressure, whereas the volume of a solid remains constant. Additionally, the volume of a gas is typically measured in units of volume per unit of mass (i.e. m3/kg), while the volume of a solid is measured in units of length cubed (i.e. cm3 or m3).

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