Asked by shel
The base of a solid is the circular region bounded by the graph of
x^2 + y^2 =a^2, where a > 0. find the volume of the solid if every cross-section perpendicular to the x-axis is a square?
x^2 + y^2 =a^2, where a > 0. find the volume of the solid if every cross-section perpendicular to the x-axis is a square?
Answers
Answered by
Anonymous
y = (a^2 - x^2)^.5
1/2 a side of square is y
so area of square at x , A(x) = 4 y^2 = 4 (a^2-x^2)
integrate that dx from x = 0 to x = a and double it for the left half
V = 2 * int(0 to a) (4 a^2 - 4 x^2) dx
= 8 [ a^3 - a^3/3 ] = (16 /3) a^3
check that, I did it fast.
1/2 a side of square is y
so area of square at x , A(x) = 4 y^2 = 4 (a^2-x^2)
integrate that dx from x = 0 to x = a and double it for the left half
V = 2 * int(0 to a) (4 a^2 - 4 x^2) dx
= 8 [ a^3 - a^3/3 ] = (16 /3) a^3
check that, I did it fast.
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.