Finding the volume of a function rotated

[e_glaud]

So the base of a solid is a circle with a radius equal to 5 units. Each cross section perpendicular to a fixed diameter of the base is semicircular. The circle is centered at the origin. This is going to be solved in terms of x

With this, how would I find the area of the cross section, and the volume of the shape? I have an idea, and it may be right, but my online homework portal is very stubborn. Thanks!

 

[stapel]

So the base of a solid is a circle with a radius equal to 5 units. Each cross section perpendicular to a fixed diameter of the base is semicircular.

Have you pictured in your head (or on paper) what is probably the shape of this solid?

The circle is centered at the origin. This is going to be solved in terms of x

How does "x" relate to the previous information. What is the "this" that "is going to be solved"? What were the instructions?

With this, how would I find the area of the cross section, and the volume of the shape? I have an idea....

Please reply with your idea. Thank you!

 

[e_glaud]

Have you pictured in your head (or on paper) what is probably the shape of this solid?


How does "x" relate to the previous information. What is the "this" that "is going to be solved"? What were the instructions?


Please reply with your idea. Thank you!

Yeah I can picture it in my head, and sorry I don't think this is meant to be rotated.

I don't really know why I included the x part, but I had solved the area of the cross section in terms of x. My idea was to create an integral from -5 to 5, with pi( 25 - x^2)^2 dx. But this did not work, so i'm lost.

The exact wording of the question is The base of a solid is a circle with radius 5. Each cross section perpendicular to a fixed diameter of the base is semicircular.

If the circle is centered at the origin and the fixed diameter lies on the x-axis, find the cross-section area A(x).

 

[e_glaud]

sorry it also asks to find the volume V of the shape

 

[stapel]

Have you pictured in your head (or on paper) what is probably the shape of this solid?

Yeah I can picture it in my head...

Great! What's that shape called?

How does "x" relate to the previous information. What is the "this" that "is going to be solved"? What were the instructions?

The exact wording of the question is:

The base of a solid is a circle with radius 5. Each cross section perpendicular to a fixed diameter of the base is semicircular.

If the circle is centered at the origin and the fixed diameter lies on the x-axis, find the cross-section area A(x).

it also asks to find the volume V of the shape

I don't really know why I included the x part, but I had solved the area of the cross section in terms of x.

Okay. Please show what you did, starting with how you defined "x", all the way to your function for the cross-sectional area A(x).

Please reply with your idea.

My idea was to create an integral from -5 to 5, with pi( 25 - x^2)^2 dx. But this did not work, so i'm lost.

What was this supposed to do? What was the meaning of this integral? (It looks like you're trying to find the area under the curve, being the cross-sectional area A(x), but you said that you'd already completed that, so this must be something else.)

Please be complete. Thank you!