Page 51 - ACE YR IGCSE A TOP APPR' TO MATHS

[ (1.5 + 9.5)50 ] = 134.058 cm 3
8 Volume = 2 × 25 Volume of the cylinder
2
= 6875 m = π × 4 × 3.5
3
= 6875000 l [3] = 175.952 cm 3
2
9 (a) Slanted height of the cone, l = √h + 9 Total volume
3
Surface area of the cone = π × 3 + π × 3 × = 309.97 cm
2
2
√h + 9 = 310 ml [5]
∼
= 9π + 3π √h + 9 (b) (i) 1 l ÷ 310 ml 3 cups [1]
2
Surface area of the hemisphere (ii) 1000 ml – (310 ml × 3) [1]
= 70 ml

= πr + 4πr 2 (c) Volume of the cylinder
2
= 3πr 2 = 250 – 134.058
2
Penerbitan Pelangi Sdn Bhd. All Rights Reserved.
2
9π + 3π√h + 9 = 3πr = 115.942 cm 3
2
√h + 9 = r – 3 115.942 = π × 4 × h
2
2
2
h + 9 = (r – 3) h = 2.306
2
2
2
h = √(r – 3) – 9 Height to the top of the cup
2
2
h = √r – 6r 2 = 5 – 2.306 [4]
4
= 2.69 cm
h = r √r – 6 12 (a) CX = BC – BX
2
2
2
2
a = 6 [7] = 5 – 2
2
2
1
(b) × 4 × π × r = 18π CX = 4.583 cm [2]
3
2 3 r = 3 [2] (b) tan ∠XCD = XD
(c) h = √3 – 6(3) CX
2
4
= 5.196 ∠XCD = tan ( 5 )
–1
Volume = 1 × π × 3 × 5.196 4.583
2
3 = 47.49° [2]
2
2
= 48.98 cm 3 [3] (c) AX = AD – XD 2
2
10 (a) ∠OBA = 90° = 7 – 5 2
The angle between a tangent and a radius is AX = 4.899
90°. [1] tan ∠ACX = AX
(b) ∠FOB = 2 × (180° – 90° – 25°) CX
= 130° ∠ACX = tan ( 4.899 )
–1
Reflex angle of ∠FOB = 360°−130° 4.583
= 230° [2] = 46.91° [4]
(c) AO = OB (d) Volume
sin ∠OAB = 1 × BD × CX × AX
AO = 8 3 2
sin 25° = 1 × 7 × 4.583 × 4.899
= 18.93 cm 3 2
AD = 18.93 + 8 = 26.93 cm [2] = 26.19 cm 3 [2]
(d) (i) Volume of the cylinder = π × 8 × 30 13 (a) (OB + 3) = 12 + OB
2
2
2
2
= 6032.6 cm [2] OB + 6OB + 9 – 144 – OB = 0
3
2
2
(ii) ED = AD × tan EAD OB = radius = 22.5 cm (shown) [3]
= 26.93 tan 25° (b) tan ∠AOB = 12
= 12.558 cm 22.5
Volume of the triangular prism ∠AOB = 28.072°
= ( EC × DA ) × 30 Perimeter of the shaded region
(
)
2
2 × 28.072
( 12.558 × 2 × 26.93 ) = 360 × 2π × 22.5 + (3 × 2) + (12 × 2)
= 2 × 30 = 52.05 cm [5]
= 10146 cm 2 [4] (c) Area of the shaded region
(iii) 10146 – 6032 ×100% = Area of ΔAOC – Area of sector AOC
)
6032 = ( 24 × 22.5 ) ( 2 × 28.072 × π × 22.5
–
2
= 68.2% [2] 2 360
11 (a) Volume of the hemisphere = 270 – 248.068
= 2 × π × 4 = 21.93 cm 2 [4]
3
3
Answers 171
Answers.indd 171 15/03/2022 11:08 AM