The diagram below shows a shape with two straight edges and one irregular edge - Leaving Cert Mathematics - Question b - 2011

Based on the estimate of the man's height (1.75 m), you can visually assess the height of the hopper tank to be approximately 4.5 metres, and the diameter to be about 3 metres.

The tank can be approximated as a cylinder with a cone above and below. The volume of a cylinder is given by the formula:

V_{cylinder} = ext{Base Area} imes ext{Height} = rac{ heta^2}{4} imes h

And the volume of a cone is given by:

V_{cone} = rac{1}{3} imes ext{Base Area} imes ext{Height}.

Taking the diameter as 3 metres:

• Radius $r = 1.5$ m, Height of cylinder $h_{cylinder} = 3$ m, and Height of conical sections $h_{cone} = 1.5$ m.
• Therefore:

V_{cylinder} = rac{ heta^2}{4} imes 3 = rac{(3)^2}{4} imes 3 = 10.69 m³.

V_{cone} = rac{1}{3} imes rac{ heta^2}{4} imes 1.5 = rac{(3)^2}{4} imes 1.5 = 3.53 m³.

Thus, total volume $V = V_{cylinder} + (2 imes V_{cone}) = 10.69 + (2 imes 3.53) = 17.75$ m³. Therefore, the estimated capacity of the tank is approximately 18 m³.