Posted by **j** on Monday, October 15, 2012 at 9:35pm.

A water trough is 4 m long and its cross-section is an isosceles trapezoid which is 210 cm wide at the bottom and 280 cm wide at the top, and the height is 70 cm. The trough is not full. Give an expression for V, the volume of water in the trough in cm^3, when the depth of the water is d cm.

- math -
**Reiny**, Monday, October 15, 2012 at 10:57pm
make a sketch of the cross-section

draw verticals from the ends of the base , to get two identical right angled triangles and a rectangle

the height of the triangle will be 70 and the top will be 35. The rectangle will be 210 by 70

Draw a water-line , let the part inside the triangle be x

and let the height of the water be d

Let's concentrate on one of the triangles.

by ratios:

x/d = 35/70

x/d = 1/2

x = d/2

Volume of water = 400( 2 triangles + rectangle)

= 400( 2(1/2)xd + 210(70) )

= 400 xd + 5880000

= 400(d/2)(d) + 5880000

= 200d^2 + 5880000 , in cm^3

## Answer This Question

## Related Questions

- Calculus - A water trough is 9 m long and has a cross-section in the shape of an...
- Differential Calculus - A water trough is 10 m long and a cross section has the ...
- calc - A water trough is 7 m long and has a cross-section in the shape of an ...
- Calculus Help Please!!! - A water trough is 5 m long and has a cross-section in ...
- Calculus - A water trough is 5 m long and has a cross-section in the shape of an...
- Calculus - A water trough is 6 m long, and its cross-section has the shape of an...
- calculus - A water-trough is 10m long and has a cross-section which is the shape...
- maths - A large canal will have a cross-section in the shape of an isosceles ...
- Math - A trough is 8 meters long, 3 meters wide, and 5 meters deep. The vertical...
- I NEED HELP PLEASE - A trough is 8 meters long, 3 meters wide, and 5 meters deep...

More Related Questions