The base of a solid in the first quadrant of the xy plane is a right triangle bounded by the coordinate axes and the line x + y = 4. cross sections of the solid perpendicular to the base are squares. what is the volume, in cubic units, of the solid?

a. 8
b. 32 divided by 3
c. 64 divided by 3
d. 64 divided by 3

64 divided by 3

Step-by-step explanation:

Data provided in the question:

Equation of line : x + y = 4

Cross-section of the base is square

Now,

From  x + y = 4

⇒ y = 4 - x

Therefore,

area of the base = ( 4 - x )² = x² + 16 - 8x

Thus,

volume , V = ₀∫⁴ [x² + 16 - 8x]dx

or

⇒ V =

or

⇒ V =

or

⇒ V =

or

⇒ V =

Hence,

Answer is 64 divided by 3

look in attachments

step-by-step explanation:

a = (-2, 0)

b= (-4, 0)

c = (-5,2)

d = (-1,2)