# Using double integral estimate how much of water can the tank contain ?

Consider a water tank modeled in pyramid shape of height $\ 4 \$ using four different planes $\ -\frac{4}{3} x-4y+z=-4 , \ 2x-4y+z=-4 , \ 2x+y+z=-4 , \ -\frac{4}{3} x+y+z=-4 \$

Using double integral estimate how much of water can the tank contain ?

Volume of pyramid $\ = \frac{1}{2} \times base \ area \times height =\frac{2}{2} \times base \ area \times 4=2 \times base \ \ area \$

So we have to find base area of the pyramid shape tank.

For this we have to find the intersection of these planes with the coordinates axes.

Let the base of the pyramid shape tank $\ ABCD \$ , then the area of the quadrilateral $ABCD \$ is our required area.

But I am unable to find this area.

Help me out.

• The volume of a pyramid is given by $\frac13 \cdot$ Base area $\cdot$ height – The Integrator Apr 29 '18 at 10:01