Question

A 10ft long horizontal through has ends in the shape of equilateral triangles. The sides of the triangle are 6ft in length. If water is being poured inside the through, find a mathematical model that expresses the volume of the water as a function of its depth

Answer 1

Volume=cross sectional area*length

C.S.A=$\frac{1}{2}bh=\frac{1}{2}b*bSin60°$

With l as length,

Volume,V=$\frac{1}{2}b*bSin60°*l$

Mathematical model will have a partial derivative with respect to l

$\frac{\partial l}{\partial b}(V)$

=$\frac{\partial l}{\partial b}(\frac{1}{2}b*bSin60°*l)$

$=\frac{1}{4}b*bSin60°*l^{2}$