CHAPTER 10: PLAN AND ELEVATION Maths Form 5 [cikgubid/MathsF5/W7-Feb 2013/Thu/KYRHG] 10.1 Key Terms Orthogonal projection - Unjuran ortogon Plan - Pelan Front elevation - Dongakan depan Side elevation - Dongakan sisi Full scale - Skala penuh Solid line - 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) CH10: Plans and elevations Orthogonal projection on a vertical plane as Orthogonal projection on a vertical plane as 1
Transcript
CHAPTER 10: PLAN AND ELEVATIONMaths Form 5
[cikgubid/MathsF5/W7-Feb 2013/Thu/KYRHG]
10.1 Key Terms
Orthogonal projection - Unjuran ortogonPlan - PelanFront elevation - Dongakan depanSide elevation - Dongakan sisiFull scale - Skala penuhSolid line - 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)
CH10: Plans and elevations
Orthogonal projection on a vertical plane as viewed from the front (X)
Orthogonal projection on a vertical plane as viewed from the side (Y)
Orthogonal projection on a vertical plane as viewed from the top
y
1
10.2 Orthogonal projectionThe 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 Orthogonal projection on a horizontal plane
Orthogonal projection on a vertical plane
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4
Orthogonal projection on a vertical plane as viewed from the side y
Orthogonal projection on a vertical plane as viewed from the front ,x
10.3 Plan
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y x
3
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
5
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The height of the pyramid is 5 cm
6
7
8
9
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10
11
12
10.4 Elevation
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x
x
x
x
10.4.1 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
2
3
4
5
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x
x
x
x
The height of the pyramid is 5 cm
6
7
The height of the prism is 4 cm
8
9
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x
x
x
x
10
11
12
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y
y
10.4.2 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
2
3
4
5
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y
y
10
y
5 cm
4 cm
6 cm
The height of pyramid is 5 cm
6
7
The height of the prism is 3 cm
8
9
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y
y
y
11
10
11
12
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y
y
y
y
12
y
3 cm5 cm
Radius of the inner cylinder= 1 cmRadius of the outer cylinder= 2 cm
10.4.3 Elevation involving hidden edgesDraw to full scale, the side elevation (Y) of the solids below.
Solid Elevation from yExample :
1
2
3
Solid Elevation from y
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4
5
6
7
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Elevation y
3
6
4
4 4
7
3
Elevation x
4
6
Plan
10. 5 Exercises
Example:
Draw to full scale
i. the plan of the solid,ii. the front elevation of the solid as seen from Xiii. the side elevation of the solid as seen from Y
Solution:
(i) (ii) (iii)
For each of the following solids, draw to full scale
CH10: Plans and elevations
4
15
iv. the plan of the solid,v. the front elevation of the solid as seen from X,vi. 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.
2
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3
4
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2 cm
18
5
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6.
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F/G
E/D
4 cm
1 cm
4 cmK/J
I/H
V
R/SQ/P
3 cm
L/M
V
Q/RP/S
K/LJ/M5 cm
3 cm
4 cm
G/DH/S/M
F/E
P/J
3 cm
4 cm 1 cm
2 cm
V
K
17.0 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.
(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.
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) (b)(ii)
1a
CH10: Plans and elevations
Diagram (i)
Diagram (ii)
22
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.
1b
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
CH10: Plans and elevations
Diagram 1(i)
Diagram 1(ii)
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.
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.
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
CH10: Plans and elevations
Diagram 2 (i)
Diagram 2(ii)
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.
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.
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.
CH10: Plans and elevations
Diagram 3(i)
Diagram 3(ii)
25
10.7 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.
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.
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 ]
CH10: Plans and elevations
Diagram 1(i)
Diagram 1(ii)
26
November 20043(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
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
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 UT as view from Y [5 marks]
CH10: Plans and elevations
Diagram 2(i)
Diagram 2(ii)
27
November 20055(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.
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.
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]
CH10: Plans and elevations
Diagram 3(i)
Diagram 3(ii)
28
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) (ii)the plan of the combined solid . [5 marks]
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6 cm
5 cm
3 cm
8 cm7 cm
4 cm
A
M
L
D
C
K
E
F
H
G
B
J
9 November 2007 You are not allowed to use graph paper to answer this question.
(a) Diagram 7(i) shows a solid right prism with rectangular base ABCD on a horizontal plane. The surface ABJHGF is the uniform cross- section of the prism. AF, HG and BJ are vertical edges. Rectangle JKLH is a horizontal plane and rectangle GMEF is an inclined plane.
Draw full scale, the plan of the solid.
CH10: Plans and elevations
[3 marks]
Diagram 7(i)
30
Diagram 7(ii)
CA
B
J
K
D
F
LG E
M
T
SH
4 cm
7 cm8 cm
5 cm
P
Q
(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).
Draw full scale,
(i) the elevation of the combined solid on a vertical plane parallel to AB as viewed from P ,
(ii) the elevation of the combined solid on a vertical plane parallel to BC as viewed from Q .
CH10: Plans and elevations
[4 marks]
[5 marks]
31
D CE
H
3 cm
5 cm
6 cm
8 cm
G
F
A
J
4cm
B
K
11 November 2008 You are not allowed to use graph paper to answer this question.
(a) Diagram 15(i) shows a solid right prism with rectangular 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.
Draw full scale, the elevation of the solid on a vertical plane parallel to AB as viewed from X .
CH10: Plans and elevations
[3 marks]
Diagram 15(i)
X
32
D
Q
E
H
3 cm
5 cm
6 cm
8 cm
G
F
A
J
4cm
B
K
RS
W U
T
(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.
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.
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