Question

Find the volume for the regular pyramid.

*drawing included*

Answer 1

V=1/3(area of base)(height)

Answer 2

Find the area of the base and multiply by the height which it looks like might be 3

Answer 3

The area of the cross section at height y is given by
\[A_y = B\left(1-\frac{y}{h}\right)^2\]
To fid the volume of the pyramid, you integrate between the y values 0 and h:
\[Vol = \int_{0}^{h}B\left(1-\frac{y}{h}\right)^2dy = \frac{B}{h^2}\int_0^h (h-y)^2dy\]
\[=\frac{B}{h^2} \int_{0}^{h}(h^2 - 2hy + y^2)dy = \frac{B}{h^2}(h^2y - hy^2 + \frac{y^3}{3}) \vert_0^h\]
\[ = \frac{B}{h^2}\left(\frac{h^3}{3}\right) = \frac{1}{3}Bh\]

So just sub in your values for the area of the base, B = 2x2/2 = 4/2=2 and for h which is 3 to find: Vol = 6/3 = 2 cubic units.