Teacher's Guide - Pearson

2. a) V a5 3 10 2 3 30 5 9 424.8 cm 3SA a5 2r 2 1 2rh 5 2 513.3 cm 2b) V b5 ​1__8 ​ 3 V 5 1 178.1 cm3aSA b5 ​1__ 5 628.3 cm2c)d)__V b​ 5 ​1__V a8 ​___SA b​ 5 ​1__SA a4 ​4 ​ 3 SA aSupport Activity 13.1 (Student’s Book page 229)1. 4:9; 8:272. 3:2; 27:83. 2:5; 4:25Activity 13.1 (Student’s Book page 230)1. a) Diameters: ___ 8​24 ​ 5 ​ 1__3 ​Surface areas: 1__9 ​Volumes: ​ ___ 127 ​Note: In the formula V 5 ​1__3 ​r2 h, both r and h are multiplied by the scale factor ​ 1__3 ​,therefore the scale factor by which the volume decreases works out to be (​ 1__3 ​)2 3 ​1__3 ​ 5 ___ ​ 127 ​.b) and c) Truncated cone surface area5 SA full cone2 SA small cone1 3 4 25 240 2 ​1__ ​ 3 240 1 1695 229​1__3 ​ ​( 8__ cm2 9 ​ 3 240 1 16 )​∴ Ratio 5 229​ 1________ 3 ​240 ​ 5 ____ ​ 688720 ​ 5 ___ ​ 4345 ​Truncated cone volume5 V full cone2 V small cone5 2304 2 ___ ​127 ​ 3 2304265 ​ ___27 ​ 3 23045 2 218 2__ ​ cm332 218​2__∴ Ratio 5 _______ 3​​2304 ​ 5 _____ ​ 6 6566 912 ​ 5 ___ ​ 2627 ​OR:Ratio 5 1 2 ​ ___ 127 ​ 5 ___ ​ 2627 ​Chapter 13: Surface area and volume73