LC Ordinary Level Solutions Set A (LC 2016) (© Educate.ie)

Question 7 (55 marks)Question 7 (a)

LC 2016 (Set A): Paper 2

r

Surface area and volume: Sphere [page 8]

A rV r=

=

4 2

343

π

π

Formulae and Tables Book

165 billion = 165 000 000 000=1∙65 × 1011

Number in Scientific notation: a n an× ∈ ≤ <10 1 10, ,�

(i) Diameter (d) = 2 × Radius (r) d = 18 m ⇒ r = 9 m

( ( )ii) Volume

m

V r= =

= = ⋅

43

43

3 3

3

9

972 3053 63

p p

p

Combined surface area

m

= ×=

=

9 4 9

2916

9161

2

2

pp( )

Question 7 (b)

Question 7 (c)

Marking Scheme NotesQuestion 7 (a) [Scale 15B (0, 4, 15)]4: Accept any one of the following: • 16·5 × 1010

• 165 × 109

• 109

• 106

• 103

• 165 000 000 000 • 1∙65

Marking Scheme NotesQuestion 7 (b) (i) [Scale 5B (0, 1, 5)]1: • Writes answer as 18

2 or similar

Question 7 (b) (ii) [Scale 5C (0, 1, 2, 5)]1: • Identifies correct volume formula • Writes answer from part (b) (i) in this section2: • Formula fully substituted correctly (consistently) • One error in substitution followed by correct calculation • Answer as 972pNote: π = 3·14, (3052∙08 m3); π = 227 , (3054∙86 m3)

Question 7 (c) [Scale 5C (0, 1, 2, 5)]1: • Identifies correct formula • Identifies radius correctly or consistently (in this part) • Indicates multiplication by 92: • Expression fully substituted • S.A. of one sphere correctly calculated.(1018 m2)Note: π = 3·14, (9156 m2); π = 227 , (9165 m2)

LC Ordinary Level Solutions Set A (LC 2016) (© Educate.ie)

Marking Scheme NotesQuestion 7 (d) (i) [Scale 5C (0, 1, 2, 5)]1: • Identifies correct formula • Identifies r = 1·65 or ℎ = 23 • Indicates multiplication by 82: • Expression fully substituted • Area of one pipe correctNote: π = 3·14, (1907 m2); π = 227 , (1908 m2)

Question 7 (d) (ii) [Scale 15C (0, 3, 5, 15)]3: • ÷ 12 indicated. • Identifies correct formula. • Indicates r = 1·45.5: • Equation fully substituted.

Question 7 (d) (ii) [Scale 5A (0, 5)]

Formulae and Tables BookSurface area and volume:

Cylinder [page 10]

h

r

A rhV r h=

=

22

p

p

r h= ⋅ == × ⋅= ⋅

=

1 65 23

8 2 1 65 23

607 2

19

m m

Combined surface areas

,

( )( )pp

008 2m

r h

h

= ⋅ =

=× ⋅ =⋅

1 45

3170

12 2 1 45 3170

34

2

m

Combined surface areas m

, ?

( )p88 3170

3170

34 829

p

p

h

h

=

∴ =⋅= m

Total surface area:9 spheres + 8 shorter cylindrical pipes + 12 longer cylindrical pipes= 9161 + 1908 + 3170= 14 239 m2

Cost of painting the Atomium at e70 per square metre = 14 239 × 70 = e996 730

Question 7 (d)(i)

(ii)

(iii)