Question

Find the volume v of the described solid s. a frustum of a pyramid with square base of side b, square top of side a, and height h

Answer 1

Use the general formula:

Volume = Height * (area of top+4*area at mid height+area at bottom) /6

Example for a cube of side s:
Vcu=s(s^2+4s^2+s^2)/6=s^3

Example for a cone of radius r
Vco=h(0+4*pi r^2/4+pi r^2)/6=pi r^2 h/3

Example for a sphere or radius r:
Vsph=2r*(0+4pi r^2 + 0)/6 = 4pi r^2 /3

So for a square frustrum with end sides a & b, height h:
Vf=h*(a^2+4((a+b)/2)^2+b^2)/6=(a^2+(a+b)^2+b^2)h/6
or simply
Vf=(a^2+(a+b)^2+b^2)h/6