Answer to Question #110559 in Geometry for atta

Question

the diagram shows a water container in the form of an inverted pyramid ,which is such that when the height of the water level is h cm the surface of the water is a square of side 1/2 h cm
1)express the volume of water in the container in term of h.
{note . the volume of a pyramid having a base area A and vertical height h is 1/3Ah

Answer 1

Answer:$\frac1{12}h^3$

$Formula\;of\;volume:\;V=\;\frac13\times A\times h\\Formula\;of\;area\;of\;square:\\A=side\times side=\frac12h\;\times\;\frac12h\;=\;\frac14h^2\\V=\frac13\times A\times h=\frac13\times\frac14h^2\times h=\frac1{12}h^3$