Observation

 

This is a question on true shape and development.  A given square prism inclined to the vertical plane and partly truncated at the top.  The candidates were expected to draw the given views and draw the complete plan, true shape of the cut surface and the development of the truncated square prism.

Many candidates attempted this question but many of them failed to draw the complete plan and the true shape.

Candidates were expected to:

A.        COPYING THE GIVEN VIEW

(i) draw the  X- Y axis;                                                 

(ii)draw the front elevation;                                           

(iii)project down from front elevation to draw the plan;       

(iv)      draw the plan.                                                 

B.        THE PLAN                                                                

(A)FIRST AUXILIARY ELEVATION

(i)draw the horizontal line AD in the front elevation;         

(ii)project down from point D to point d in the plan;          

(iii)join points a to d and extend the line ad;

(iv)draw lines from points b and c parallel to ad respectively;                                         

(v)drawX1 – Y1 axis perpendicular to  projected lines from points a, b, and c;

(vii)transfer corresponding coordinates from front elevation on X – Y axis to X1 – Y1 axis and locate points b1, a1d1 and c1 to draw the  first auxiliary elevation;        

(viii)join the points b1, a1d1 and c1 to obtain the  first auxiliary elevation.

 

TRUE SHAPE (SECOND AUXILIARY PLAN)

(i)draw lines from the points b1, a1 d1 and c1 perpendicular to line b1  c1;

(ii)draw X2- Y2 axis parallel to lines b1 c1;                

(iii)transfer corresponding coordinates from plan on X1- Y1 axis  to lines on X2- Y2  axis to locate the points a2, b2 and c2 for the true shape;

(iv) join the points a2, b2 and c2 to  obtain the true shape.     

 C.       MEASURING AND STATING THE LENGTHS AND ANGLE:

(i)State the lengths of the true shape of the triangle as a2b2 = 60+ 1; b2c2 = 57 +1 and  c2b2 = 90 +1;                      

(ii)        State the angle of inclination of the triangle to the plane as (HP) = 53o+ 1o horizontal.                                                                                                                           
The solution is shown below: