#### Q20: A cone of base diameter 50 mm and axis 60 mm is resting on its base on the H.P. A section plane perpendicular to V.P. and inclined at 45^{0} to H.P., bisects the axis of the cone. Draw the development of its lateral surface.

**Solution:**

**Steps :**

(i) Here generators *o* ‘2’, *o* ‘3’, *o* ‘4’, *o* ‘6’, *o* ‘7 ‘ and *o* ‘8’ are not of the true length. Therefore, intersection points on these generators need to be projected on the generator *o*‘1’ which is of true length. Point *b* ‘, *c* ‘, *d* ‘ ……*e* ‘ are thus projected as *b* “, *c* “, *d* “….. on generator *o* ‘1’.

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- The angle subtended by an arc at the center is given as,
^{r}_{s}^{0}. - Where,
*s*slant height of cone = 65 mm*o*‘1’ ,*r*_{Theta = 25/ 65}X 360= 138.5^{0}- Mark point
*O*and draw an arc of circle of radius =*o*‘1’ with angle 5^{0}. Divide the arc 1*o*1 into 8 equal parts.- Mark point
*A*on*O*1 such that*OA o*‘*a*‘ and point*B*on*O*2 such that*OB O*‘*b*“. Similarly, mark point*C*,*D*,*E*,*F*,*G*and*H*on*O*3,*O*4,*O*5,*O*6,*O*7 and*O*8

- Mark point

- Draw smooth curve passing through points
*A*,*B*,*C*,*D*….. etc.

- Mark point

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