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

Answer 1

when x=0 : y = 2
when y = 0: x= 4

Correct answer is 2pi/3

Answer 2

radius = 2

i believe they mean forming a sphere, if you can imagine a 2d circle with a radius of 2 being "circled" about (for lack of a better word) around a 3d axis to create a sphere.

the volume of a sphere is 4/3pi*r^3, which would make the volume of this sphere (32/3)pi

Answer 3

Volume = (1/2) *1/3 (3.14) (R)^2 (H)
V = (1/2) 1/3 (3.14)(1)^2 (4)
V = 4pi/6
2 pi/3