section of solid and development of surfaces m. s. shinge...development of surface at the side of...
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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
Section of Solid And Development of Surfaces M. S. Shinge
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
development of surface.
MSS
Section of Solid And Development of Surfaces M. S. Shinge
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
Section of Solid And Development of Surfaces M. S. Shinge
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
Section of Solid And Development of Surfaces M. S. Shinge
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
Section of Solid And Development of Surfaces M. S. Shinge
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
Section of Solid And Development of Surfaces M. S. Shinge
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.
Q1 Determine reference plane, to
which given section plane is
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
Section of Solid And Development of Surfaces M. S. Shinge
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.
Q1 Determine reference plane, to
which given section plane is
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
Section of Solid And Development of Surfaces M. S. Shinge
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.
Q1 Determine reference plane, to
which given section plane is
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
Section of Solid And Development of Surfaces M. S. Shinge
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.
Q1 Determine reference plane, to
which given section plane is
perpendicular
HP Edge view of section plane will be seen in TV.
Q2 Inclination with VP 45
0
Q3 Location of section plane
10 mm away from axis
𝜃 =𝐷
𝐿× 1800 = 1210
MSS
Section of Solid And Development of Surfaces M. S. Shinge
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.
Q1 Determine reference plane, to
which given section plane is
perpendicular
HP Edge view of section plane will be seen in TV.
Q2
Inclination with VP
Parallel to VP
Q3 Location of section plane
15 mm away from axis
MSS
Section of Solid And Development of Surfaces M. S. Shinge
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.
Q1 Determine reference plane, to
which given section plane is
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
development of surface.
MSS
Section of Solid And Development of Surfaces M. S. Shinge
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
Section of Solid And Development of Surfaces M. S. Shinge
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.
Q1 Determine reference plane, to
which given section plane is
perpendicular
VP Edge view of section plane will appear in FV.
Q2 Inclination with HP ?
Q3 True shape of section isosceles triangle
MSS