<p>Hello, I have an AP Calculus BC question that I need help on.
The base of a solid is the region bounded by the parabola y^2 = 4x and the line x = 2. Each plane section perpendicular to the x-axis is a square. The volume of the solid is
(A) 6 (B) 8 (C) 10 (D) 16 (E) 32
I do not understand the sentence "Each plane section perpendicular to the x-axis is a square." Can anyone please explain this problem for me?</p>
<p>(The answer is E)</p>
<p>If you took the base and rotated it to form a solid and took a slice of the solid, it would be a square. The height of the section is the same as the width.</p>
<p>"Each plane section perpendicular to the x-axis is a square." Ok if its perpendicular to the x-axis, draw a vertical thin rectangle. if its a scuare, then the rectangle is a base for one of the squares, which you have to visualize growing up from the paper. Nothing rotates here, remember. Draw the picture: limits of integration are x=0 and x=2. the inside of the integral is (sqrt(4X)^2), or just 4x. So it's int from 0 to 2 4x dx. Which turns out to be 8, which is weird.</p>
<p>Thank you Patrick and vladimir.
I'm sorry but, I am still confused. I understand the question now but I keep getting the answer B. My answer is the same as that of vladimir. The book claims that the answer is E. Can anyone please clarify this problem?</p>