PLAN AND ELEVATION 17.1 Key Terms Orthogonal projection Plan Front elevation Side elevation Full scale Solid line
-
Unjuran ortogon Pelan Dongakan depan Dongakan sisi Skala penuh Garis penuh ( used to draw visible edge)
Dashed line
-
Garis putus-putus (used to draw invisible edge)
Fine solid line
-
Garis penuh yang halus (used to show projection/ construction line)
Orthogonal projection on a vertical asonviewed Orthogonalplane projection a vertical viewed from from plane the asfront (X) the front (X)
Orthogonal projection on a Orthogonal verticalprojection planeonas a viewed vertical plane as viewed from from the side (Y) the side (Y)
X Y
y Orthogonal Orthogonal projection on a vertical plane as viewed from projection on a the top vertical plane as viewed from the top
Plans and elevations
1
17.2 Orthogonal projection The orthogonal projection of an object is a two dimensional or flat image of the object. The image is formed by looking at perpendicular lines, that is , the normal coming from the object and intersecting the plane of view. Tick ( √ ) the correct orthogonal projections
1
Orthogonal projection on a horizontal plane
2
Orthogonal projection on a horizontal plane
Orthogonal projection on a vertical plane
3
Plans and elevations
Orthogonal projection on a horizontal plane
2
Orthogonal projection on a vertical plane
Orthogonal projection on a vertical plane as viewed from the side y
4
y
x
Orthogonal projection on a vertical plane as viewed from the front ,x
Plans and elevations
3
17.3 Plan The orthogonal projection of a solid on a horizontal plane as viewed from the top of the object is known as plan. Draw to full scale, the plans of the solids below. 1
2
3
4
Plans and elevations
4
5
The height of the pyramid is 5 cm 6
5 cm
4 cm
7
8
Plans and elevations
5
9
3c
m
10
6
cm
2
cm
2 cm
6 cm
11
12
Plans and elevations
6
17.4 Elevation 17.4.1 Front Elevation The orthogonal projection of a solid on a vertical plane as viewed from the front of the object is known as front elevation. Draw to full scale, the front elevation,(x) of the solids below 1
x 2
x 3
x
4
x
Plans and elevations
7
5
x The height of the pyramid is 5 cm 6
7
x
x The height of the prism is 4 cm 8
x
Plans and elevations
8
9
3c
m
x 10
6
cm
2
cm
2 cm
6 cm
x 11
x 12
x
Plans and elevations
9
17.4.2 Side Elevation The orthogonal projection of a solid on a vertical plane as viewed from the side of the object is known as side elevation. Draw to full scale, the side elevation (Y) of the solids below
1
y
2
y
3
y
4
y
Plans and elevations
10
5 y
The height of pyramid is 5 cm
6 y
7 y
The height of the prism is 3 cm
8
y 6c
Plans and elevations
m
11
9
y 3c
m
y
6
cm
2
4 cm
cm
10
11
y
12
y
Plans and elevations
12
17.4.3 Elevation involving hidden edges Draw to full scale, the side elevation (Y) of the solids below. No
Solid
Elevation from y
Example :
1
2
3
3 cm
5 cm
y
Radius of the inner cylinder= 1 cm Radius of the outer cylinder= 2 cm
Plans and elevations
13
Solid
Elevation from y
4
5
6
7
Plans and elevations
14
17. 5 Exercises Example: Draw to full scale i. ii. iii.
the plan of the solid, the front elevation of the solid as seen from X the side elevation of the solid as seen from Y
Solution:
(i)
(ii)
(iii)
4
4 4
6
3
3 7 4
4 6 Plan
Plans and elevations
Elevation x
15
Elevation y
For each of the following solids, draw to full scale iv. v. vi.
the plan of the solid, the front elevation of the solid as seen from X, the side elevation of the solid as seen from Y.
1. A cylinder of radius 2 cm is removed from the centre of a cuboid. The remaining solid is shown in the diagram below.
Plans and elevations
16
2
Plans and elevations
17
3
2 cm
4c m
Plans and elevations
18
cm
4
cm
2
2 cm
4 cm
4
Plans and elevations
19
5
Plans and elevations
20
6.
Plans and elevations
21
17.6 Questions according to examination format Example : (a)Diagram (i) below shows a solid consisting of a right prism and a right pyramid which are joined at the plane, PQRS. The base, JKLM, is placed on horizontal plane. PJKQ is the uniform cross-section of the prism. PJ and SM are vertical edges. The height of the pyramid is 4 cm. Draw the full-scale elevation of the solid on the vertical plane parallel to JK as viewed from X.
Diagram (i) (b) A solid cuboid is joined to the solid in Diagram (i) at the vertical plane, LMSR. The combined solid is shown in Diagram (ii). The square base, JKED, is on a horizontal plane.
Diagram (ii) Draw the full-scale (i) the plan of the combined solid, (ii) elevation of the combined solid on a vertical plane parallel to LE as viewed from Y Solution (a)
(b)(i)
V
P/S
3 cm
Plans and elevations
5 cm
I/H
Q/P 2 cm 4 cm
K/L
22
1 cm
F/G
4 cm
Q/R
K J/M
V
G/D
V
3 cm
4 cm
H/S/M
P/J
(b)(ii)
F/E 1 cm
R/S
3 cm K/J
4 cm
L/M
E/D
3
cm
4 cm
5
cm
1a
Diagram 1(i)
The above diagram shows a solid which consists of two prisms whose base ABPQRCD lies on a horizontal table. PU = CV = 6 cm and W is the mid-point of PU. The length of PQ is 7 cm. Draw to full scale, the elevation of the solid on a vertical plane parallel to QR as viewed from Y.
3
cm
5
cm
1b
Diagram 1(ii) A semi-cylinder is joined to the solid. Draw to full scale, i. the plan of the solid ii. the elevation the solid on a vertical plane parallel to DR as viewed from x
Plans and elevations
23
2(a). Diagram 2 (i) shows a solid right prism with the rectangular base, PQRS, resting on a horizontal table. EFGHQP is the uniform cross section of the prism. Rectangle EFLM is an inclined plane. Rectangle GHJK is a horizontal plane. EP, FG and HQ are vertical edges.
Diagram 2 (i) Draw the full scale plan of the solid. 2(b) A solid cuboid is joined to the prism in Diagram 2(i) at the vertical plane, MSUZ. The combined solid is shown in Diagram 2(ii) . The base PQRUVWS, is on a horizontal plane and AB = BC = 2 cm.
Diagram 2(ii) Draw the full scale (i) elevation of the combined solid on a vertical plane parallel to PQ as viewed from X (ii) elevation of the combined solid on a vertical plane parallel to QR as viewed from Y
Plans and elevations
24
3(a) Diagram 3(i) shows a solid prism with its rectangular base, PQRS, on a horizontal table. The surface, FGKLRQ, is the uniform cross-section of the prism. Rectangle EFGH is an inclined plane and rectangle JKLM is a horizontal plane. FQ, KG and LR are vertical edges.
Diagram 3(i) Draw the full scale elevation of the solid on a vertical plane parallel to QR as viewed from X. 3(b) A solid right prism with the uniform cross-section, ITU, is removed from the solid in Diagram 3(i) . The remaining solid is shown in Diagram 3(ii). Rectangle TFVU is a horizontal plane. IU is a vertical edge. FT = 3 cm and IU = 2 cm.
Diagram 3(ii) Draw the full scale (i) plan of the remaining solid (ii) elevation of the remaining solid on a vertical plane parallel to PQ as viewed from Y.
Plans and elevations
25
17.7 Past Year SPM Questions November 2003 1(a) Diagram 1(i) shows a solid right prism with rectangular base FGPN on a horizontal table. EFGHHJK is the uniform cross-section of the prism. Rectangle EKLM is an inclined plane. Rectangle JHQR is a horizontal plane. EF,KJ and HG are vertical edges.
Diagram 1(i) Draw to full scale the plan of the solid .
[3 marks]
(b) A solid cuboid is joined to the prism in the Diagram 1(i).at the vertical plane PQRLMN. The combined solid is as shown in the Diagram 1(ii). The square base FGSW is horizontal.
Diagram 1(ii) Draw full scale (i) the elevation of the combined solid on a vertical plane parallel to FG as viewed from C, [ 4 marks ] (ii) the elevation of the combined solid on a vertical plane parallel to GPS as viewed from D. [5 marks ] Plans and elevations
26
July 2004 2(a) Diagram 4(i) shows a solid right prism with rectangular base ABCD on a horizontal table. The surface ABLKGF is the uniform cross section of the prism. Rectangle EFGH is an inclined plane and rectangle JKLM is a horizontal plane. AF, GK and BL are vertical edges and GK = 2 cm.
Diagram 4(i) Draw full scale, the elevation of the solid on a vertical plane parallel to AB as viewed from X. [ 3 marks ] (b) Another solid right prism is joined to the prism in Diagram 4(i) at the vertical plane CVJQ. The combined solid is as shown in Diagram 4(ii). Quadrilateral PQCW is the uniform cross section of the prism. rectangle WCRU is an inclined plane and the square TPWU is a horizontal plane. The base ABRSQD lies on a horizontal table, KL = JM = 3 cm and GK = 2 cm.
Diagram 4(ii)
Draw full scale, ( i ) the plan of the combined solid [ 4 marks] ( ii ) the elevation of the combined solid on a vertical plane parallel to BCR as viewed from Y [ 5 marks]
Plans and elevations
27
November 2004 3(a) Diagram 2(i) shows a solid consisting of a cuboid and a half cylinder which are joined at the plane HJMN. The base GDEF is on a horizontal plane and HJ=3 cm
Diagram 2(i)
Draw to full scale, the elevation of the solid on a vertical plane parallel to DG as viewed from X. [3 marks ] (b) A solid right prism is joined to the solid in Diagram 2(i) at the vertical plane ELMW. The combined solid is as shown in diagram 2(ii). Trapezium PMWU is the uniform cross-section of the prism and PQRM is an inclined plane. The base DEUTSWFG is on a horizontal plane and EU= 2cm
Diagram 2(ii) Draw to full scale, (i) the plan of the combined solid (ii) the elevation of the combined solid on a vertical plane parallel to UT as view from Y
Plans and elevations
28
[4 marks] [5 marks]
July 2005 4(a) Diagram 5(i) shows a solid right prism with rectangular base ABCD on a horizontal table. The surface ABLKGF is the cross-section of the prism. Rectangle GKJH is an inclined plane. Rectangles JKLM and EFGH are horizontal planes. AF and BL are vertical edges.
Diagram 5(i) Draw full scale, the plan of the solid
[ 3 marks]
(b) Another solid cuboid is joined to the prism in Diagram 5(i) at the vertical plane DPJHE. The combined solid is as shown in Diagram 5(ii). The base ABBCPQV lies on a horizontal table.
Diagram 5(ii) Draw full scale, ( i) the elevation of the combined solid on a vertical plane parallel to BC as viewed from X, (ii) the elevation of the combined solid on a vertical plane parallel to AB as viewed from Y.
Plans and elevations
29
[4 marks] [5 marks]
November 2005 5(a) Diagram 3(i) shows a solid right prism with rectangular base PEFN on a horizontal table. The surface EFGHJ is the uniform cross section of the prism. Rectangle KJHL is an inclined plane and rectangle LHGM is a horizontal plane. JE and GF are vertical edges.
Diagram 3(i) Draw full scale, the elevation of the solid on a vertical plane parallel to EF as viewed from X . [ 3 marks ] (b) A solid right prism with uniform cross section UVWX is removed from the solid in Diagram 3(i). The remaining solid is as shown in Diagram 3(ii) rectangle VSTW is a horizontal plane. UV and XW are vertical edges. VS=3 cm and SE= 2 cm.
Diagram 3(ii) Draw full scale, (i) the plan of the remaining solid [ 4 marks] (ii) the elevation of the remaining solid on a vertical plane parallel to PE as viewed from Y . [ 5 marks]
Plans and elevations
30
July 2006 6. (a) Diagram 7(i) shows a solid right prism with rectangular base ABCD on a horizontal plane. The surface ABHGF is its uniform cross section. The rectangle EFGK is an inclined plane and the square GHJK is a horizontal plane.The edges AF and BH are vertical.
Draw to full scale, the elevation of the solid on a vertical plane parallel to AB as viewed from X . [ 3 marks ] (b) Another solid right prism is joined to the solid in Diagram 7(i) at a vertical plane CJKL to form a combined solid as shown in Diagram 7(ii). Trapezium KLMS is its uniform cross section. The rectangle KSRQ is an inclined plane. The edges KL and SM are vertical. The base ABCMNPLD is on a horizontal plane.
Draw to full scale, (i) the plan of the combined solid, [ 4 marks] (ii) the elevation of the combined solid on a vertical plane parallel to ME as viewed from Y. [ 5 marks] Plans and elevations
31
SPM Nov 2006 7(a) Diagram 8(i) shows a solid right prism. The surface KLSR is its uniform cross section. The base JKLM is a rectangle on a horizontal plane. The rectangle JKRQ is an inclined plane and the square QRST is a horizontal plane. The edges SL and TM are vertical.
Draw to full scale, the elevation of the solid on a vertical plane parallel to LK as viewed from X . [ 3 marks ] (b) Another solid right prism is joined to the solid in Diagram 8(i) at the vertical plane KLSG to form a combined solid as shown in Diagram 8(ii). The trapezium ABCD is its uniform cross section and AFKB is an inclined plane The rectangle ADEF is a horizontal plane. The base JKBCLM is on a horizontal plane. The edge DC is vertical.
Draw to full scale, (i) the elevation of the combined solid on a vertical plane parallel to JB as viewed from Y [ 4 marks] (ii) the plan of the combined solid . [ 5 marks]
Plans and elevations
32
8 SPM Jul 2007 You are not allowed to use graph paper to answer this question. (a) Diagram 6(i) shows a solid right prism with rectangular base FGRQ on a horizontal plane. EFGHJKLM is the uniform cross-section of the prism. Rectangles EMNP, LKUV and JHST are horizontal planes. FE , LM , KJ and GH are vertical edges. EM = LK = JH = 2 cm. P
N
6 cm V E
S
U
2 cm M
T
Q 3 cm
R
5 cm
J H
L
K
3 cm
F 6 cm
G
Diagram 6(i) A
Draw full scale, the elevation of the solid on a vertical plane parallel to FG as viewed from A. [3 marks]
Plans and elevations
33
(b) Another solid right prism is joined to the solid in Diagram 6(i) at the vertical plane PQRSTUVN . The combined solid is shown in Diagram 6(ii). Right-angled triangle XYZ is its uniform cross-section of the prism. The base FGRWQ lies on a horizontal plane and FQW is a straighf line. X 3 cm Y 2 cm P
Z N
6 cm W
E
M
S
U
V
2 cm
T
Q 3 cm
5 cm
R J H
L
K
F 6 cm
Draw to full scale,
3 cm B
G
Diagram 6(ii)
(i) the plan of the combined solid,
[4 marks] (ii) the elevation of the combined solid on a vertical plane parallel to GR as viewed from B . [5marks]
Plans and elevations
34
9 November 2007 You are not allowed to use graph paper to answr this question. (a) Diagram 7(i) shows a solid right prism with rectanglular base ABCD on a horizontal plane. The surface ABJHGF is the uniform crosssection of the prism. AF , HG and BJ are vertical edges. Rectangle JKLH is a horizontal plane and rectangle GMEF is an inclined plane. M 3 cm E
G
L
6 cm K
F 5 cm
D
H
4 cm J
A
C 7 cm
8 cm B Diagram 7(i)
[3 marks] Draw full scale, the plan of the solid.
Plans and elevations
35
(b) A half-cylinder solid of diameter 6 cm is joined to the prism in Diagram 7(i) at the plane SKLT . The length of SK is 4 cm . The combined solid is shown in Diagram 7(ii). M
E
G
L F
K
T H
5 cm
D
4 cm
S J
C A 7 cm
8 cm B P
Q
Diagram 7(ii)
Draw full scale, (i)
the elevation of the combined solid on a vertical plane parallel to AB as viewed from P ,
[4 marks]
(ii) the elevation of the combined solid on a vertical plane parallel to BC as viewed from Q . [5 marks]
Plans and elevations
36
10 Jun 2008 You are not allowed to use graph paper to answr this question. (a) Diagram 15(i) shows a solid right prism. The rectanglular base ABCD lies on a horizontal plane. The rectangle ABGF is an inclined plane. Trapezium ADEF is the uniform cross-section of the prism. The edges DE is vertical . 3 cm
H
E
G
F 4 c
C 3 cm 5 cm D
A
5 cm Diagram 15(i)
Draw to full scale, the plan of the solid.
Plans and elevations
37
[3 marks]
(b) Another solid right prism is joined to the solid in Diagram 15(i) at the vertical plane DCHE . The composite solid is shown in Diagram 15(ii). Pentagon QPNMR is the cross-section of the prism. PJKN is an inclined plane and NKLM is a horizontal plane The base ABCSRQD lies on a horizontal plane. The edges RM and QP are vertical. MN = QD = 2 cm and PQ = 6 cm. J
L
K H
P
7 cm
E
M
G
F
N
C
S
B
4 cm
5 cm D
R
4 cm
X
5 cm
A
Q
Diagram 15(ii)
Draw to full scale (i)
the elevation of the composite solid on a vertical plane parallel to RQ as viewed from X, [4 marks] (ii) the elevation of the composite solid on a vertical plane parallel to AB as viewed from Y . [5 marks]
Plans and elevations
38
Y
11 November 2008 You are not allowed to use graph paper to answr this question. (a) Diagram 15(i) shows a solid right prism with rectanglular base ABHG on a horizontal plane.The surface ABCDE is the uniform cross-section of the prism. AE and BC are vertical edges. Rectangle DEFK is an inclined plane and rectangle CDKJ is a horizontal plane. K 3 cm
F
J 5 cm
G H
E
D
C
4cm A
6 cm
8 cm
B
X Diagram 15(i)
Draw full scale, the elevation of the solid on a vertical plane parallel to AB as viewed from X .
Plans and elevations
39
[3 marks]
(b) A solid cuboid is cut and removed from the solid in Diagram 15(i). The remaining solid is shown in Diagram 15(ii). Rectangle QRST is a horizontal plane. SB = 2 cm, UT = 3 cm and ST = 4 cm.
K 3 cm
F
J 5 cm
G W Q E
D
H
U T 8 cm
4cm
Y R
A
S 6 cm
B
Draw to full scale, (i) the plan of the remaining solid, (ii) the elevation of the remaining solid on a vertical plane parallel to BH as viewed from Y .
[4 marks]
[4 marks]
Plans and elevations
40
ANSWERS Orthogonal projection
Plan
Front Elevation, X
Side Elevation Y
1
1
1
1
2
2
2
2
3cm 4 cm
3
3
3 5cm
5cm
6cm
3
4
6cm
4
4
5
5
6
6
5 cm
5
4
6
5cm 4cm
4cm
7
5 cm
7
5cm
7
6cm
Orthogonal projection
Plan
Front Elevation, X
Side Elevation Y
1
1
1
1
2
2
2
2
3cm 4 cm
3
3
3 5cm
5cm
6cm
3
4
6cm
4
4
5
5
5 cm
5
Plans and elevations
41
4
6
6
5cm
6
4cm
4cm
7
5cm
5 cm
7
7
8
8
9
9
6cm
8 6cm
9
4cm 3 cm
10
10
10
11
11
11 6 cm
6cm 3 cm
12
12
17.43 Elevation involving hidden sides 1. 2
3
12
1
2
4
1
3 5
5
Plans and elevations
6
7
42
Plan
Front elevation, X
Side elevation, Y
1
2
8 cm
6 cm
3
2 cm
3 cm
2 cm
1 cm
1 cm
3 cm
5 cm
3 cm
4 cm
4 cm
2 cm
4 cm
6 cm
4
5
3 2 1
Plans and elevations
43
6 4
4 cm
3
2 cm 2 cm
4 cm 6
1 a.
6 cm
b.
c.
Y-elevation
Plan
2 (a)
X-elevation
(b)(i) 4 cm
(b)(ii)
1 cm 2 cm 1 cm
4 cm
1 cm 1 cm
3 cm
1 cm 4 cm
3 cm
3
6 cm 6 cm
4 cm 2 cm
2 cm 6 cm
3 cm
3 cm 2 cm
2 cm 10 cm
Plans and elevations
2 cm
44
17.7 SPM past years questions 1) SPM2003(N)
V/U 1(b)(i)
5 cm
2 cm
X/T
2 cm
M,N E/M 5 cm
5 cm
5 cm
J/R
2 cm
R
J
F/N/W
2 cm
7 cm
Q/P
H/G 1(b) (ii)
X//L/V
K
T/U
2 cm M
E
7 cm
3 cm Q/R
H/J 2 cm G/F
Plans and elevations
5 cm
P/N 2 cm
45
S/W
G/P/S
2 SPM2004(Julai)
3 cm
(a)
(b) (i)
2cm
2 cm
2 cm
5 cm
3 cm 4 cm
4 cm
6 cm 6 cm b(ii)
4 cm 7cm
2 cm
3 cm
4 cm
2cm
3 SPM2004(Nov)
3 cm
(a)
2 cm
3 cm
6 cm
Plans and elevations
46
(b) (i)
N/F
H/G 3 cm M/W
J
R/S
3 cm 5 cm K/D
L/E
4 cm
P/U
b(ii)
2 cm
P
Q/T
2 cm
Q 2 cm
K/J/H
L/M/N
R
3 cm
D/G
U/E/W/F 4 cm
T/S
4 SPM 2005(Julai) (a)
Plans and elevations
47
(b) (i)
(ii)
Plans and elevations
48
5 SPM 2005(Nov)
J,K
G,M
H,L 7 cm
4 cm
E,P (b)(i)
L
K,P
U,V
K
L,M
M,N
X,W
S,E 3 b(ii)
F,N
8 cm
H,T U
X
H,G
S,T
V,W
P,N Plans and elevations
G,F
E,F 49
6 SPM 2006(Julai)
Plans and elevations
50
7 SPM 2006(Nov)
Plans and elevations
51
SPM 2007(Jun)
SPM 2007(Nov)
Plans and elevations
52
SPM 2008(Jun)
SPM 2008(Nov)
Plans and elevations
53
