the area of the trapezium?

Question

in a factory,watse liquid is poured into cylindrical drums. The area of the base of each drum is 2000cm squared and the height is 90cm.
Calculate
(a)the volume of each drum giving your answer in cubic meters
(b) when full,the drums are emptied into a tank.Both the base of the tank,DCGH and its top,ABFE,are horizontal rectangles.Each vertical sides ABCD and EFGH is a trapezium
(i)Find the area of the trapezium ABCD
(ii)the volume of the tank
(c)how many full drums of watse can be emptied into the tank?

Answer 1

If you are having problems with the volume of the cylinder, check out:
http://en.wikipedia.org/wiki/Cylinder_%28geometry%29

Since the base and the top of the tank are horizontal rectangles, I assume you mean the sides are what Americans refer to trapezoids - quadrilaterals with two parallel sides.

http://en.wikipedia.org/wiki/Trapezoid

And, in this case, I assume these trapezoids are all symmetric.

You don't give us the tank dimensions so we can't answer parts b and c numerically.

To find the area of the trapezoid, there are a number of approaches. Let a be the longer horizontal, b the shorter, and c the length of the "vertical"sides.

Let h be the unknown height of the trapezoid (in the plane of the side, not the 3D height from top to base). Then the area is h(a + b)/2.

But it is also the area of a rectangle b x h plus the area of a triangle with sides (a-b) x c x c.

Given the three sides of the triangle, we can compute its area with method 4 from:
http://www.btinternet.com/~se16/hgb/triangle.htm

Using the result and the formula for method 1, we can compute the height.

With the height we can compute the area of the rectangle.

For the volume you also need the 3D height of the tank. Play the same game on a vertical cross-section (as opposed to the slanted trapezoids) which is also a trapezoid. Its horizontals are a and b as before, but its vertical sides are the heights of the side trapezoids.