Page 1 :
Exercise 13.6, , 99 7, ' _ 2 unless stated otherwise., e Assume T = 7 |, , ni. \The circumference of the base of a cylindrical, , ‘ Vag, 5 cm. How many litres of water cay, , Questio i |, , 132 cm and its height is 2, (1000cm* 2 41.), , Solution We have, circumference of the base = 132cm, , enr = 132, 2x oe r= 132, re 132 x7, , 22x 2, , r=21cm, , Volume of cylinder = mr2h= 2 x 21x 21x 25, , \, , , , , , = 34650 cm?, (Given, 1000 cm? = 1L, 1 cm? a, = 34650 cm? = 34890 ,, 1000, = 34.65 L, , witvtion 2. The inner diameter, $ outer diameter is 28 cm, Th, , Pe if 1em? of wood, Solution Given, inn, , of a cylindrical wooden pipe 8°, e length of the pipe is 35 cm.", has a mass of 0.6 g., , Inner fadius (r er diameter = 24 cm, , Ws 12cm, Outer diameter — 28 ¢, ‘Bem
Page 3 :
“ , sy, the lateral surface of a cylinder is 94 9 cn’, 5, , Question * then find. “tit |, , . + of its base,, , (i) radius © (ise 2 = 3,14), , ey 2 lume., (ii) its vo intern 4, ave, lateral surface of a cylinder = 94.2 cm? ang h=B on, , . Weh, Solution onrh = 94.2, “ 2x 314xrx5 = 94.2, = = 942 |, 3 31.4, , r=3em, =>, , (i) Hence, radius of base, r = 38cm, = nh = 3.14(3)* x5, , =314x 9x5, . =14130m°, , (ii) Volume of acylinder, Question 5. It costs ¢ 2200 to paint the inner curved surface of a!, cylindrical vessel 10 m deep. If the: cost of painting is at the rate of, , %20 per m’, find, (i) inner curved surface area of the vessel, i, (ii) radius of the base, . 4, (uti) capacity of the vessel. °, , Solution We have,.cost to paint the inner curved surface = 2200, , Cost to paint per m? = 20 ‘, Cost to paint the inner curved surfac, , Inner curved surface area = ¢, Cost to paint per m, , , , 2 mh = & 2200, %20, , 2 ‘, 2x xr x10=110, , = 110m., , , , — 110x7, 2x 220, , r, , , , _7, (i) Inner Cur [= 4 1.75, , (ii) Henes - 9 Surt, ) Hence, rage area of the vessel = 110m?, , Sana niy TMS, {ili) Capacity of the. ‘he base is 1.75 m,, , Ve, ‘sel = Volume of the vessel, =nr°h, = kA 77 77, KK eas, 7 ior x 10 3, = 96.25 'm?
Page 4 :
1 ion 6. The capacity of a closed cylindrical y i i, ‘izes. How many square metres of metal shat would beat, , ve it?, ion Capacity of a closed cylindrical vessel = 15.4 L, , , , , , , , , , , , , , = 15.4 x 1000cm* ted, AL = 1000 ern?, mr?h = 15400 cm? ane, , nmr? x 100 = 15400, 2. 7, ilar (sh = 1m=100cm), r?=7x7, r=7com, . suriace area of closed cylindrical vessel = 2nr(--+h), , = 2x 2x79 +100), , = 44x 107 = 4708 cr?, 4708.2, , 100x 100, = 0.4708 m?, , &netal sheet must be required = (1cem= io m), 100, , ion 7. A lead pencil consists of a cylinder of wood with a solid, er of graphite filled in the interior. The diameter of the pencil is, mand the diameter of the graphite is 1 mm. If the length of the, ilis 14 cm, find the volume of the wood and that of the graphite., , ion Diameter of the graphite cylinder= 1 mm = + em (: imm= = cm), , Radius, r = a cm, 20, , ‘, , Volume of the graphite cylinder = mreh= ae:, = 041m, , th of the graphite, h = 14cm, (F~ ly cling 14 )om*, , fi iz, diameter of the pencil =7mm= a cm, , . 7, Radius of the pencil, r= a, length of the pencil, h= » 9, . 3 fog 3 3, Volume of the pencil = mrchs (; x 20 x 30 x 14 om =5.39 m, , ood = Volume of the pencil — Volume of the graphite, , = (5.39- 0.11) cm?, =528cm", , je of w
Page 5 :
wiry, , . . . ‘ : . ‘ 0!, estion 8. A patient ina hospital is given soup daily in a cylindieat, om of diameter 7 cm. If the bowl is filled with soup to a height of a “, , how much soup the hospital has to prepare daily to serve 259 Patio.”, Solution We have, diameter = 7cm io), , Radius, r = Som, , h=4cm, Capacity of the cylindrical bowl = Volume of the cylinder = mr2h, = 22. v x io x4, 7 2, , = 22x 7 = 154 cm?, Volume of soup to be prepared daily to serve 250 patients, , = 154 x 250 cm® = 38500 cm?, , _ 38500 stad, , |, i, 1000 1000, , = 38.5L
