Volume Expression

nch · #1 $Old$ October 18th, 2009, 04:20 PM

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.

skeeter · #2 $Old$ October 18th, 2009, 04:38 PM

Quote:

Originally Posted by nch $View Post$

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.

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

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

note that $\frac{x}{d} = \frac{1}{2}$ by similar triangles

nch · #3 $Old$ October 18th, 2009, 04:56 PM

so this is the equation i get
V= 19.2d+480d
= 499.2d^2
is that correct ??
could you please help me find the expression
thank you.

skeeter · #4 $Old$ October 18th, 2009, 05:22 PM

Quote:

Originally Posted by nch $View Post$

so this is the equation i get
V= 19.2d+480d
= 499.2d^2
is that correct ??
could you please help me find the expression
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.

aidan · #5 $Old$ October 19th, 2009, 06:15 AM

Quote:

Originally Posted by nch $View Post$

so this is the equation i get
V= 19.2d+480d
= 499.2d^2
is that correct ??
could you please help me find the expression
thank you.

Just a curious question:
How did you get 19.2d ?

also
this:
19.2d + 480d
should result in:
(499.2)d