Section of Solid And Development of Surfaces M. S. Shinge...development of surface at the side of true length of edge. MSS Section of Solid And Development of Surfaces M. S. Shinge

Section of Solid And Development of Surfaces M. S. Shinge

Page 1

1. Draw the development of lateral surface of the hexagonal pyramid as shown in figure.

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Solution 1:

2. Hexagonal

Pyramid, Base

side 25 mm; Axis

height 70 mm

1. Cone

Front view of generators o’1 and o’5 are

in true length form because top view of

generators o’1 and o’5 are parallel to XY

line i.e. to VP. So select side of

generator o’1 or o’5 to draw

development of surface.

𝜃 =𝐷

𝐿× 1800 = 1390 MSS


Page 2

Solution 2:

3. A pentagonal base prism with base side of 25 and one side parallel to VP stand on HP. It carries a

hole of 40 mm diameter. At center of 50 mm axis of prism, such that hole axis is perpendicular to

VP. Complete the development of lateral surfaces of prism.

4. A cylinder with base diameter of 50 mm is resting on base on HP. It is cut by a square hole side

25 mm, its sides equally inclined to HP and axis perpendicular to VP at center of 70 mm axis of

cylinder. Complete the development of lateral surfaces of cylinder.

Front view of generators o’1 and o’4 are

in true length form because top view of

generators o’1 and o’5 are parallel to XY

line i.e. to VP. So select side of

generator o’1 or o’4 to draw


MSS


Page 3

Solution 3:

Solution 4:

Length of development of surface = Perimeter

of pentagon = 25 × 5 = 125𝑚𝑚

Length of development of surface = Circumference

of cylinder base = 𝜋 × 𝐷 = 157𝑚𝑚

MSS


Page 4

5. A

cylinder

of base

dia. 40

mm and

height

60 mm

is

resting

on HP.

It is cut

by

section

plane

perpen-

dicular

to VP,

inclined

at 450 to

HP and passing through the point on the axis 15 mm below the circular top. Draw FV, sectional TV

and true shape of section also development of remaining part.

6. A triangular base prism with base side of 60 mm and one side parallel to VP stand on HP. It is

cut by a hole of 40 mm diameter at center of 90 mm axis of prism, such that hole axis is

perpendicular to VP. Complete the development of lateral surfaces of prism.

MSS


Page 5

7. A square base prism with base side of 40 mm and two sides equally inclined to VP stand on HP.

It is cut by a hole of 20 mm diameter at center of 80 mm axis of prism, such that hole axis is

perpendicular to VP. Complete the development of lateral surfaces of prism.

MSS


Page 6

8. A pentagonal pyramid with base side 30 mm and axis 60 mm long is resting on its base on

ground, having an edge of base parallel to FRP. It is cut by a section plane, which is perpendicular

to FRP and inclined at 450 to HRP and passing through a point on the axis, 25 mm above the base.

Draw its front view, sectional top view and true shape of section.

Q1 Determine reference plane, to

which given section plane is

perpendicular

FRP Edge view of section plane will appear in FV.

Q2 Inclination with HRP 45

0

Q3 Location of section plane passing through a point on the axis, 25 mm above the

base

Front views of both outside slant edges (o’1

and o’4) are not in true length formbecause

their top views are not parallel to XY line i.e. to

VP. To find out true length of slant edge

rotate any edge to make parallel to XY line and

project in front view. Draw development of

surface at the side of true length of edge.

MSS


Page 7

9. A hexagonal base pyramid with base side 25 mm and axis 55 mm long is resting on its base on

HRP, having an edge of base perpendicular to FRP; it is cut by cutting plane which is

perpendicular to HRP and at 450 with FRP and passing through the base of pyramid at a distance

of 10 mm away from the axis. Draw its sectional FV; top view and true shape of section. Also draw

development of remaining part.



perpendicular

HRP Edge view of section plane will be seen in TV.

Q2 Inclination with FRP 45

0

Q3 Location of section plane passing through the base of pyramid at a distance of 10

mm away from the axis

Front views of outside slant edges are not in

true length formbecause their top views are not

parallel to XY line i.e. to VP. To find out true

length of slant edge rotate any edge to make

parallel to XY line and project in front view. Draw

development of surface at the side of true

length of edge.

MSS


Page 8

10.A hexagonal pyramid of base side 30 mm and axis is 70 mm stands on HP with two sides parallel

to VP. It is cut by section plane 450 to VP and passing 12 mm away from axis. Draw sectional front

view, top view and true shape of section. Also draw development of surface.



perpendicular

HP Edge view of section plane will be seen in TV.

Q2 Inclination with VP 45

0

Q3 Location of section plane passing 12 mm away from axis

Front view of longer edgeso’a and o’d are in true

length form because their top views are parallel to

XY line i.e. to VP. Select side of slant edgeo’a or

o’d to draw development of surface.

MSS


Page 9

11. A cone of base diameter 40 mm and height 60 mm is resting on HP. It is cut by section plane

perpendicular to VP, inclined at 600 to HP and passing through the point on the axis 15 mm from

the apex. Draw front view, sectional top view, and true shape of section also development of

remaining part of cone.



perpendicular

VP Edge view of section plane will be seen in FV.

Q2 Inclination with HP 60

0

Q3 Location of section plane passing through the point on the axis 15 mm from the

apex

𝜃 =𝐷

𝐿× 1800 = 1140

MSS


Page 10

12. A right circular cone of base diameter 50 mm and axis 70 mm stands on HP. It is cut by AVP

which makes an angle 450 to VP and 10 mm away from axis. Draw sectional front view, top view

and true shape of section. Also draw development of surface.



perpendicular


Q2 Inclination with VP 45

0

Q3 Location of section plane

10 mm away from axis

𝜃 =𝐷

𝐿× 1800 = 1210

MSS


Page 11

13. A right circular cone of base diameter 80 mm and height 90 mm is resting on base in HP. It is

cut by section plane parallel to VP and at a distance of 15 mm in front of axis of cone. Draw

sectional front view, top view, and development of remaining part of cone.



perpendicular


Q2

Inclination with VP

Parallel to VP

Q3 Location of section plane

15 mm away from axis

MSS


Page 12

14. A pentagonal base pyramid with base side 25 mm and height 50 mm is resting on HP. with one

of its base edge perpendicular to VP. It is cut by section plane 450 HP and passing through its LHS

corner. Draw FV, sectional TV, and true shape of section also development of remaining part of

pyramid.



perpendicular

VP Edge view of section plane will appear in FV.

Q2 Inclination with HP 45

0

Q3 Location of section plane Passing through its LHS corner.

Front view of longer edgeo’4

is in true length form because

its top views isparallel to XY

line i.e. to VP. Select side of

slant edge o’4 to draw


MSS


Page 13

15. An ant starts from the extreme left base corner of right circular cones back to same point after

travelling around it by the shortest route. Trace out the shortest path of the ant on FV and TV of

the cone, having base diameter 60 mm and axis height 80 mm.

An ant starts from the extreme left

base corner of right circular cones

back to same point after travelling

around it by the shortest route

Shortest route from 1 to 1 on development of cone is

straight line joining 1 and 1.

Draw development of surface.

Shortest route from 1 to 1 is straight

line 1-1. Mark intersecting points of

line 1-1 and generators on

development of surface and project

in front view and top view.

MSS


Page 14

16. A cone of base diameter 60 mm and axis 70 mm long is resting on its base in HRP. It is

cut by AIP so that true shape of section is an isosceles triangle having 50 mm base. Draw

F.V., sectional TV and true shape of section.



perpendicular

VP Edge view of section plane will appear in FV.

Q2 Inclination with HP ?

Q3 True shape of section isosceles triangle

MSS

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Section of Solid And Development of Surfaces M. S. Shinge...development of surface at the side of true length of edge. MSS Section of Solid And Development of Surfaces M. S. Shinge