CALC 3: volume of sphere x^2+y^2+z^2<=9 between z=1, z=2

[fredericoahb]

Dear all, i have problems with this question, someone can show the complete solution? The original question is in portuguese, i tried to translate and i sent the original question attached. Thanks

which the volume of the ball of the equation x² + y² + z² <= 9 that lies between the planes z = 1 and z = 2.

 

[Deleted member 4993]

Dear all, i have problems with this question, someone can show the complete solution? The original question is in portuguese, i tried to translate and i sent the original question attached. Thanks

which the volume of the ball of the equation x² + y² + z² <= 9 that lies between the planes z = 1 and z = 2.

What are your thoughts?

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[fredericoahb]

CALC 3: volume of a sphere

Dear all, i have problems with this question, someone can show the complete solution? The original question is in portuguese, i tried to translate and i sent the original question attached. Thanks

which the volume of the ball of the equation x² + y² + z² <= 9 that lies between the planes z = 1 and z = 2.

im tryint to solve the following equation. Is that right?

 

[SAMUELK]

im tryint to solve the following equation. Is that right?

It might be right, but easier would be to do volumes of revolution by slices, or disks. (probably section 9.7 in your text)

Do it by taking x^2 + y^2 = 9, from x = 1 to x = 2, [yes, I said 'x'],
then rotating about the x-axis.

Each disk has height(the radius) = srqt(9 - x^2)
Each has thickness (height of disk) = dx

Volume = pi r^2 h = pi (srqt(9 - x^2))^2 dx

= pi (9 - x^2) dx

Integrate from x = 1 to x = 2

I got 20pi/3; is that one of the choices?

 

[fredericoahb]

It might be right, but easier would be to do volumes of revolution by slices, or disks. (probably section 9.7 in your text)

Do it by taking x^2 + y^2 = 9, from x = 1 to x = 2, [yes, I said 'x'],
then rotating about the x-axis.

Each disk has height(the radius) = srqt(9 - x^2)
Each has thickness (height of disk) = dx

Volume = pi r^2 h = pi (srqt(9 - x^2))^2 dx

= pi (9 - x^2) dx

Integrate from x = 1 to x = 2

I got 20pi/3; is that one of the choices?

Yes, that's the answer. Very good sotution. Thanks