# Volume Expression

• Oct 18th 2009, 02:20 PM
nch
Volume Expression
A water trough is 4 m long and its cross-section is an isosceles trapezoid which is 120 cm wide at the bottom and 180 cm wide at the top, and the height is 60 cm. The trough is not full. Give an expression for V, the volume of water in the trough in cm3, when the depth of the water is d cm.
• Oct 18th 2009, 02:38 PM
skeeter
Quote:

Originally Posted by nch
A water trough is 4 m long and its cross-section is an isosceles trapezoid which is 120 cm wide at the bottom and 180 cm wide at the top, and the height is 60 cm. The trough is not full. Give an expression for V, the volume of water in the trough in cm3, when the depth of the water is d cm.

$\displaystyle V = 4A$ , where $\displaystyle A$ = cross-sectional area of water

$\displaystyle A = \frac{d}{2}[(1.2+2x)+1.2]$

note that $\displaystyle \frac{x}{d} = \frac{1}{2}$ by similar triangles
• Oct 18th 2009, 02:56 PM
nch
so this is the equation i get
V= 19.2d+480d
= 499.2d^2
is that correct ??
thank you.
• Oct 18th 2009, 03:22 PM
skeeter
Quote:

Originally Posted by nch
so this is the equation i get
V= 19.2d+480d
= 499.2d^2
is that correct ??
thank you.

no, that is not correct.

remember that your units have to match.

you have everything you need to find the volume formula in terms of d.
• Oct 19th 2009, 04:15 AM
aidan
Quote:

Originally Posted by nch
so this is the equation i get
V= 19.2d+480d
= 499.2d^2
is that correct ??