1. A square pyramid with a 40mm base and 65mm axis is cut by a section plane perpendicular to the vertical plane and inclined at 45 degrees to the horizontal plane, bisecting the axis. 2. The problem requires drawing the sectional top view, sectional side view, and true shape of the section. 3. The solution involves constructing projectors and finding intersection points to determine the outlines of the cut section in each view.

1. Section of Solids
(step-by-stepprocedure)
by
Dr T Ravi Kiran
Professor, ME, LNCT, Bhopal

2. Q 1: A square pyramid, base 40 mm side and axis 65 mm long, has its base on the HP and all the
edges of the base equally inclined to the VP. It is cut by a section plane, perpendicular to the VP,
inclined at 45º to the HP and bisecting the axis. Draw its sectional top view, sectional side view
and true shape of the section.
X
450
a
b
c
d
o
a’
b’
c’
d’
Y
1. Since the pyramid is resting on HP with base equally inclined, the t.v. will be a square
equally inclined with xy line.
2. Draw both f.v. and t.v. with 2H pencil; as it is not evident at this stage the cut-out or left-
out portions of the pyramid.

3. Q 1: A square pyramid, base 40 mm side and axis 65 mm long, has its base on the HP and all the
edges of the base equally inclined to the VP. It is cut by a section plane, perpendicular to the VP,
inclined at 45º to the HP and bisecting the axis. Draw its sectional top view, sectional side view
and true shape of the section.
X
450
a
b
c
d
o
a’
b’
c’
d’
o’
Y
1. Locate the apex o’ which is at a distance of 65 mm from xy line along the projector from O
2. Now, join the extreme base points a’ and c’ with o’
3. Since when viewed from bottom, b is clearly visible; therefore o’-b’ will be a thick line.
65

4. Q 1: A square pyramid, base 40 mm side and axis 65 mm long, has its base on the HP and all the
edges of the base equally inclined to the VP. It is cut by a section plane, perpendicular to the VP,
inclined at 45º to the HP and bisecting the axis. Draw its sectional top view, sectional side view
and true shape of the section.
Y
450
a
b
c
d
o
a’
b’
c’
d’
o’
1’
2’
3’
4’
X
1. Since the cutting plane is perpendicular to VP; it will look like a line in the f.v. The section
plane passes through mid point of the axis. So, locate the mid point of line o’-b’
2. Now draw a chain line at 45o passing through mid point of axis. Note that the cutting plane
line is thick at the end and thin in between. Name the intersection points as 1’, 2’ etc.

5. Q 1: A square pyramid, base 40 mm side and axis 65 mm long, has its base on the HP and all the
edges of the base equally inclined to the VP. It is cut by a section plane, perpendicular to the VP,
inclined at 45º to the HP and bisecting the axis. Draw its sectional top view, sectional side view
and true shape of the section.
X Y
a
b
c
d
o
a’
b’
c’
d’
o’
1’
3’
4’
1. Now, darken the lower portion of the pyramid in the f.v. as is left out after removing
the top portion.

6. Q 1: A square pyramid, base 40 mm side and axis 65 mm long, has its base on the HP and all the
edges of the base equally inclined to the VP. It is cut by a section plane, perpendicular to the VP,
inclined at 45º to the HP and bisecting the axis. Draw its sectional top view, sectional side view
and true shape of the section.
X Y
45º
a
b
c
d
o
a’
b’
c’
d’
o’
1
2
3
4
1’
2’
3’
4’
1. Draw projections from 1’ & 3’ on lines oa and oc to intersect at pt 1 & 3.
2. Since there is no possibility of intersection of 2’ & 4’ with lines ob & od; therefore pt 2’ is
projected on O’1’ & in turn on line oa. This point is then shifted with centre O as shown.

7. Q 1: A square pyramid, base 40 mm side and axis 65 mm long, has its base on the HP and all the
edges of the base equally inclined to the VP. It is cut by a section plane, perpendicular to the VP,
inclined at 45º to the HP and bisecting the axis. Draw its sectional top view, sectional side view
and true shape of the section.
X Y
45º
a
b
c
d
o
a’
b’
c’
d’
o’
1
2
3
4
1’
2’
3’
4’
1. All the points obtained from projections from the cutting plane are joined with straight
lines(1-2-3-4). This section is hatched i.e.,thin equidistant lines are drawn using 2H pencil.
2. The remaining portion of the solid is then darkened using thick lines (a-1,2-b, 3-c & 4-d).
1-2-3-4 is known sectional top view.
3. The hatch lines should make 45o
or 135o with XY line.

8. Q 1: A square pyramid, base 40 mm side and axis 65 mm long, has its base on the HP and all the
edges of the base equally inclined to the VP. It is cut by a section plane, perpendicular to the VP,
inclined at 45º to the HP and bisecting the axis. Draw its sectional top view, sectional side view
and true shape of the section.
X Y
45º
a
b
c
d
o
a’
b’
c’
d’
o’
1
2
3
4
1’
2’
3’
4’
X1
Y1
d” a” c” b”
o”
1. To draw side view, X1Y1 is drawn perpendicular to XY line at a suitable distance.
2. Projectors from the f.v. & t.v. of the pyramid is drawn . The projectors from the t.v. are
drawn horizontal upto the line X1Y1 & then rotated about point P as shown.
P

9. Q 1: A square pyramid, base 40 mm side and axis 65 mm long, has its base on the HP and all the
edges of the base equally inclined to the VP. It is cut by a section plane, perpendicular to the VP,
inclined at 45º to the HP and bisecting the axis. Draw its sectional top view, sectional side view
and true shape of the section.
X Y
45º
a
b
c
d
o
a’
b’
c’
d’
o’
1
2
3
4
1’
2’
3’
4’
X1
Y1
d” a” c” b”
o”
3”
2”
4”
1”
1. Draw projectors from pt 1’ to meet o’’a’’ at point 1’’. Repeat the same for 2’, 3’ & 4’

10. Q 1: A square pyramid, base 40 mm side and axis 65 mm long, has its base on the HP and all the
edges of the base equally inclined to the VP. It is cut by a section plane, perpendicular to the VP,
inclined at 45º to the HP and bisecting the axis. Draw its sectional top view, sectional side view
and true shape of the section.
X Y
45º
a
b
c
d
o
a’
b’
c’
d’
o’
1
2
3
4
1’
2’
3’
4’
X1
Y1
d” a” c” b”
o”
3”
2”
4”
1”
1. Join 1’’-2’’-3’’-4’’ with thick lines and hatch it using parallel lines with uniform gap of 3-5
mm at an angle of 45o or 135 with xy line.
2. Darken the lower portion of the pyramid using thick lines as shown. This fig is known as
sectional side view.

11. Q 1: A square pyramid, base 40 mm side and axis 65 mm long, has its base on the HP and all the
edges of the base equally inclined to the VP. It is cut by a section plane, perpendicular to the VP,
inclined at 45º to the HP and bisecting the axis. Draw its sectional top view, sectional side view
and true shape of the section.
X Y
45º
a
b
c
d
o
a’
b’
c’
d’
o’
1
2
3
4
1’
2’
3’
4’
11
41
21 31
X1
Y1
d” a” c” b”
o”
3”
2”
4”
1”
1. Draw projectors perpendicular to the cutting plane line in the front view as shown.
2. Mark point 11 on projector from 1’ in taking distance of pt 1 from xy line. Similarly mark
pts 21 , 31 & 41

12. Q 1: A square pyramid, base 40 mm side and axis 65 mm long, has its base on the HP and all the
edges of the base equally inclined to the VP. It is cut by a section plane, perpendicular to the VP,
inclined at 45º to the HP and bisecting the axis. Draw its sectional top view, sectional side view
and true shape of the section.
X Y
45º
a
b
c
d
o
a’
b’
c’
d’
o’
1
2
3
4
1’
2’
3’
4’
11
41
21 31
X1
Y1
d” a” c” b”
o”
3”
2”
4”
1”
1. Join 11 -21 -31 -41 with thick lines and hatch it using thin lines. The is section is known as
true shape.