Question

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

Answer 1

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 = $[\frac{x^3}{3}+16x -\frac{8x^2}{2}]_0^4$

or

⇒ V = $[\frac{4^3}{3}+16(4) -\frac{8(4)^2}{2}]-[\frac{0^3}{3}+16(0) -\frac{8(0)^2}{2}]$

or

⇒ V = $[\frac{64}{3}+64 -64]-0$

or

⇒ V = $\frac{64}{3}$

Hence,

Answer is 64 divided by 3