determine the volume of the regular solid bodies from given data?

Question

if its cross-section is a trapiezium, calculate the maximum volume of waste material it can hold when filled up level to its brim.

http://i10.photobucket.com/albums/a121/TurboD15/DSC00507.jpg

do u work out area of trapezium first?

1/2 * sum of parallel sides * height

0.5 * 13 * 5 = 32.5cm squared?

how u work out the volume?

how do you work out the volume of this shape?

http://i10.photobucket.com/albums/a121/TurboD15/DSC00510.jpg

Answer 1

You have a good idea on how to compute the area of the side correctly.

To compute the volume multiply the area of the side by the depth

V=.5(a+b)x c x h

V=.5(5+8)x 2 x 3=39 m^3

Similarly for the second sahpe

V=.5xaxbxc
V=.5 x 12 x 5 x 4=120 cm^3

Answer 2

You are on the right track.

Let the trapezium have sides of length a cm and b cm and perpendicular distance between sides of h cm.

The area of this trapezium is given by A = (1/2 ) h (a + b) cm²

If the distance between the trapeziums is L, the volume is then calculated from V = AL cm³

So you are indeed correct in that you can work out the area of a trapezium and then multiply by the distance between the two trapeziums.

Good luck!

Answer 3

It's easy to work out the trapezium's volume using integral calculus. Work out the area of a horizontal cross section, multiply by dy and perform a definite integral. Ta-da.