Answer:
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 = [tex][\frac{x^3}{3}+16x -\frac{8x^2}{2}]_0^4[/tex]
or
⇒ V = [tex][\frac{4^3}{3}+16(4) -\frac{8(4)^2}{2}]-[\frac{0^3}{3}+16(0) -\frac{8(0)^2}{2}] [/tex]
or
⇒ V = [tex][\frac{64}{3}+64 -64]-0[/tex]
or
⇒ V = [tex]\frac{64}{3}[/tex]
Hence,
Answer is 64 divided by 3
