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| 1. |
A cistern |
| Answer» GivenVolume of cistern = {tex}150 \\times 120 \\times 110 \\mathrm { cm } ^ { 3 } = 1980000 \\mathrm { cm } ^ { 3 }{/tex}Volume of water =\xa0129600 cm3Volume of one brick =\xa0{tex}22.5 \\times 7.5 \\times 6.5 \\mathrm { cm } ^ { 3 } = 1096.875 \\mathrm { cm } ^ { 3 }{/tex}Each brick absorbs one - seventeenth of its volume of waterVolume of water absorbed by one brick = {tex}\\frac { 1 } { 17 } \\times{/tex}\xa0volume of brick = {tex}\\frac { 1 } { 17 } \\times 1096.875 \\mathrm { cm } ^ { 3 }{/tex} = 64.52 cm3Let n be the total number of bricks which can be put in the cistern without water overflowing. Then,Volume of water absorbed by n bricks =\xa0{tex}n \\times \\frac { 1 } { 17 } \\times 1096.875 \\mathrm { cm } ^ { 3 }{/tex}{tex}\\therefore{/tex} Volume of water left in cistern =\xa0{tex}= \\left( 129600 - \\frac { n } { 17 } \\times 1096.875 \\right) \\mathrm { cm } ^ { 3 }{/tex}Since the cistern is filled upto the brim.Therefore, Volume of the cistern =\xa0Volume of water left in the cistern + Volume of bricks\xa0{tex} 1980000{/tex} =\xa0{tex}129600 - \\frac { n } { 17 } \\times 1096.875 + n \\times 1096.875 {/tex}{tex}n \\times 1096.875 - \\frac { n } { 17 } \\times 1096.875 = 1980000 - 129600{/tex}{tex}1096.875 \\times \\left( n - \\frac { n } { 17 } \\right) = 1850400{/tex}{tex}1096.875 \\times \\frac { 16 n } { 17 } = 1850400{/tex}{tex}17550 \\times \\frac { n } { 17 } = 1850400 \\Rightarrow n = \\frac { 1850400 \\times 17 } { 17550 } = 1792.41 {/tex}since the number of bricks cannot be in decimalstherefore, required number of bricks = 1792 | |