Question

the base of a solid is the region in the first quadrant bounded by the line x+2y=4 and the coordinate axes. what is the volume of the solid if every cross section perpendicular to the x-axis is a semicercle. why is the height 4 and the radius 1? and why times (1/3) to get 2pi/3?

Answer 1

height is 4 because of the radius of the circle. rdius is 1 because the height is 4. time 1/3 gets 2 pi/3 because 1/3 times pi * 2 is 2 is 2pi/3

Answer 2

i mean why aren't the radius 2 and height 2. why times 1/3?

Answer 3

well when you integrate the limits are from -infinity to infinity so you need to multiply by 1/3 to reduce infinity by 1/3. the radius is important at 1 beause when you take 1/3 and times 1 you still get 1/3 which implies 1/3 * 2 * pi = 2pi/3