# A playing top (lattu) made up of wood has volume 231 cm 3 . it is shaped like a cone surmounted by a hemisphere of radius 3.5 cm. find the total height of the top

2
by sel7vrrubzniholmara

2016-04-04T16:09:49+05:30

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Volume of hemisphere = 2/3πr³ = 2/3×22/7×3.5×3.5×3.5 = 90cm³
volume of cone = volume of top - volume of hemisphere
volume of cone = 231 - 90 = 141 cm³ = 1/3πr²h
π = 22/7 , r= 3.5
h = (141×3×7)/(22×3.5×3.5)
h = 11
height oh the top = 11 + 3.5 = 14.5 cm
2016-04-04T16:15:05+05:30

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Volume of the playing top = volume of cone + volume of hemisphere
⇒ 231 = 2/3π r³ +1/3 Πr²h
231 =1/3πr²( 2r+h)
231= 1/3 × 22/7 ×3.5 × 3.5 [ 2 × 3.5 + h ]
231 = 7.3 × 1.75 [ 7+h]
231 = 12.8 [ 7+ h]
231 = 89.6 + 12.8 h
231- 89.6 = 12.8 h
141.4 = 12.8 h
h      = 11.04
therefore the height of the playing top is 11.04 cm