Problem 8.10 Development of Surfaces of Solids – One cuboid of side of 40 mm x 60 mm x 40 mm is resting on its longer side on H.P. & one of the longer surfaces of the cuboid is parallel to V.P .It is cut by a cutting plane which is perpendicular to V.P. and inclined to H.P. such that it passes diagonally from one corner of the top to the opposite corner of the bottom. Develop the lateral surface of the cuboid.
Step-1 Draw a horizontal x-y line of some suitable length.
Step-2 Draw a rectangle of side of 60 mm x 40 mm below the x-y line at some suitable distance from it, such that two shorter sides of the rectangle should be perpendicular with the x-y line as shown in the figure. Give notations on it. It is top view of the cuboid.
Step-3 From the center of the rectangle in the top view, draw a vertical center line of length 40 mm from the x-y line as shown in the figure. And from the all notations of the rectangle draw vertical projectors of length 40 mm from the x-y line as shown in the figure. It is a rectangular shape. And Give the notations on it. It is front view of the cuboid.
Step-4 Draw a diagonal form one corner of the top to the opposite corner of the bottom of the rectangle as shown in the front view.
Step-5 Draw a line from the top of the rectangle in the front view exactly parallel with the x-y line, and make a vertical line between the x-y line and the line drawn from the top of the rectangle at some suitable distance from the line d’-c’, as shown in the figure. And give the notations A on it as per the figure given above. From the point A, divide the x-y line in the 4 divisions in such a way that the distance of first part should be of 60 mm and then 40 mm, 60 mm and 40 mm respectively.
Step-6 Then give the notations on it in capital letters like, A, B, C etc. as shown in the figure, connects these all the points with light straight lines, these are the vertical edges of the cuboid. It is a rectangle. And it is the development of the vertical surface of the cuboid.
Step-7 Now transfer the distances of the cutting portion of the front view in the development of the cuboid at appropriate places, which can be known by the notations of the vertical edges, as shown in the prism. Then connects these points in sequence by medium dark straight lines as shown in the figure.
Step-8 This is the development of the vertical surface of the cuboid.
Step-9 Give the dimensions by any one method of dimensions and give the notations as shown into the figure.