Find the volume of the solid generated by revolving the shaded region about the x-axis. The volume of the solid is cubic units. (Type an exact answer, using n as needed.)

given equation is 4x+3y =24

=>y=8-(4/3)x

=>y=4*(2-(1/3)x)

for x intercept ,y=0

0=4*(2-(1/3)x)

(1/3)x=2

x=6

volume generated by rotating the given region about x axis by washer method v=∫_{[0 to 6]}π[4*(2-(1/3)x)]² dx

v=∫_{[0 to 6]}16π[2²-2*2*(1/3)x +((1/3)x)²] dx

v=∫_{[0 to 6]}16π[4-(4/3)x +(1/9)x²] dx

v=_{[0 to 6]}16π[4x-(4/3)(1/2)x² +(1/9)(1/3)x³]

v=_{[0 to 6]}16π[4x -(2/3)x² +(1/27)x³]

v=16π[4*6 -(2/3)6² +(1/27)6³] - 16π[4*0 -(2/3)0² +(1/27)0³]

v=16π[4*6 -(2*36/3) +(216/27)]

v=16π[24 -24 +8]

v=128π

volume =128π=402