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
Answer:
Step-by-step explanation:
The purple circle, not ring is pi 7 squared = 153.93804
Then subtract the smaller circles area (pi 4 squared) = 153.9... - 103.6725576 =
50.2654824
Purple ring is 50.2654824
The entire circle is 4+3+3 (10) squared times pi = 314.1592654
( 50.2654824 / 314.1592654 ) x 100 = 15.999999998 %
3/10+ 2/5
= 3/10+ 4/10 (common denominator is 10)
= 7/10
The final answer is 7/10~
The angle passes 90 degrees plus an additional 55 degrees
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