Asked by Justin
The base of a solid is the circle x^2 + y^2 = 9. Cross sections of the solid perpendicular to the x-axis are squares. What is the volume, in cubic units, of the solid?
A. 18
B. 36
C. 72
D. 144
Please help. Thank you in advance.
A. 18
B. 36
C. 72
D. 144
Please help. Thank you in advance.
Answers
Answered by
oobleck
the solid is symmetric, so you just find the volume of the right side and double it.
Think of the solid as a stack of thin square sheets of thickness dx. The base of each square sheet has side 2y, where y = √(9-x^2), so its area is 4y^2=4(9-x^2)
Now just integrate to add up the volumes of all those thin squares.
Think of the solid as a stack of thin square sheets of thickness dx. The base of each square sheet has side 2y, where y = √(9-x^2), so its area is 4y^2=4(9-x^2)
Now just integrate to add up the volumes of all those thin squares.
Answered by
Justin
Okay, so for the integral, I got 4(9x- 1/3x^3) + C.
Answered by
bobpursley
so for x=3, volume= 4(27-9)=4(18)=72
Answered by
oobleck
actually, you forgot to double it. You found the volume of the right half only.
v = ∫[-3,3] 4(9-x^2) dx = 2∫[0,3] 4(9-x^2) dx = 144
v = ∫[-3,3] 4(9-x^2) dx = 2∫[0,3] 4(9-x^2) dx = 144