Finding Volume of Solid with Rectangle Cross-Sections | Geometry Homework

[Chas3down]

Homework Statement

Find the volume of the solid whose base is the region bounded by the lines x=0, y=0, and y= 3*(4-x)^1/2 and whose corss-sections perpendicular to the x-axis are rectangles whose heights are two times the base.

Homework Equations

b*h

The Attempt at a Solution

The function ends at 4, so limits are 0 to 4.
Height is 2x base
so we have 2b^2

4
∫2*(3(4-x)^1/2)^2
0

And then solve the definite integral, I believe that is correct.

 

[Dick]

Homework Statement

Find the volume of the solid whose base is the region bounded by the lines x=0, y=0, and y= 3*(4-x)^1/2 and whose corss-sections perpendicular to the x-axis are rectangles whose heights are two times the base.

Homework Equations

b*h

The Attempt at a Solution

The function ends at 4, so limits are 0 to 4.
Height is 2x base
so we have 2b^2

4
∫2*(3(4-x)^1/2)^2
0

And then solve the definite integral, I believe that is correct.

Looks correct to me as well.