Answer:
Volume = 16 unit^3
Step-by-step explanation:
Given:
- Solid lies between planes x = 0 and x = 4.
- The diagonals rum from curves y = sqrt(x) to y = -sqrt(x)
Find:
Determine the Volume bounded.
Solution:
- First we will find the projected area of the solid on the x = 0 plane.
A(x) = 0.5*(diagonal)^2
- Since the diagonal run from y = sqrt(x) to y = -sqrt(x). We have,
A(x) = 0.5*(sqrt(x) + sqrt(x) )^2
A(x) = 0.5*(4x) = 2x
- Using the Area we will integrate int the direction of x from 0 to 4 too get the volume of the solid:
V = integral(A(x)).dx
V = integral(2*x).dx
V = x^2
- Evaluate limits 0 < x < 4:
V= 16 - 0 = 16 unit^3
V=4/3π r^3
(3/4)V=π r^3
3V/4π = r^3
third root√(3V/4π)
<span><span>Hope this helps!
</span>and May the Force Be With You
</span><span>
-Jabba</span>
