# Problem 8.7 Development of Surfaces of Solids

Problem 8.7 Development of Surfaces of Solids – A cylinder of diameter 50 mm and axis height 60 mm is resting on its base on H.P.  And one square hole of size 25 mm is cut through the cylinder such that the axis of the square hole is parallel to H.P. perpendicular to V.P. and in the center of the vertical axis of the cylinder. And the sides of the square hole are equally inclined with the H.P. Develop the lateral surface of the cylinder.

## Procedure:

Step-1 Draw a horizontal x-y line of some suitable length.

Step-2 Draw a circle of radius 25 mm below the x-y line at some suitable distance from it. Divide this circle into 4 equal divisions as shown in the figure. Give notations on it. It is top view of the cylinder.

Step-3 From the center of the circle in the top view, draw a vertical center line of length 60 mm from the x-y line as shown in the figure. And from the all notations of the circle draw vertical projectors of length 60 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 cylinder.

Step-4 Draw a square of length of side 25 mm and in such a way that all the sides of the square should be equally inclined with the x-y line. And the horizontal center line should be passing though the midpoint of the vertical center line of the cylinder.

Step-5 Draw a line from the top of the cylinder 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 cylinder at some suitable distance from the line c’, as shown in the figure. And give the notations A on it as per the figure given above. From the point A draw another vertical line at the distance equal to πD, where D= Diameter of the circle in the top view.

Step-6 Then divide this rectangle in 4 equal divisions, because of the 4 divisions of the circle. 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 generators of the cylinder. It is a rectangle. And it is the development of the vertical surface of the cylinder.

Step-7 Now from the cutting points of the profile with the respective vertical generators of the cylinder in the front view, draw horizontal light parallel lines, up to the respective generators in the development of the vertical surface of the cylinder. Then connect the respective points either with medium dark straight lines or medium dark free hand curves, depending on the cutting profile of the cylinder given in the front view.

Step-8 This is the development of the vertical surface of the cylinder.

Step-9 Give the dimensions by any one method of dimensions and give the notations as shown into the figure.