Alarge statue is in the shape of a square pyramid. each side of the base of the square pyramid is 723 feet long and the height is 341 feet.

what is the volume of the statue?

enter your answer in the box.

ft³

a pyramid with square base. the side of square is labeled as 723 feet. the height of pyramid is labeled as 341 feet. a dotted line represents perpendicular line from top vertex to square surface.

Look to the coefficients on the middle terms (-4x and 2y)

divide each coefficient by 2 and square to determine what to add.

(-4/2)^2 = 4 needs to be added to complete the square for x.

(2/2)^2 = 1 needs to be added to complete the square for y.

add to both sides of the equal sign to keep the equation balanced.

x^2 - 4x + 4 + y^2 + 2y + 1 = b + 4 + 1
factor
(x - 2)^2 + (y + 1)^2 = b + 5

The general equation for a circle is:
(x - h)^2 + (y - k)^2 = r^2
with center (h,k) and radius r

compare this to the equation. you see that the center is: (2, -1)

we can write
r^2 = b + 5
given that r = 7
49 = b + 5
49 - 5 = b
44 = b