A cistern,internally measuring 150 ,cm times | vedclass

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(D) The total volume of the cistern is $V_{cistern} = 150 	imes 120 	imes 110 = 1980000 \,cm^3$.The volume of water already present is $129600 \,cm^

Vedclass · Accepted Answer

$1792$

Vedclass · Answer

(D) The total volume of the cistern is $V_{cistern} = 150 	imes 120 	imes 110 = 1980000 \,cm^3$.The volume of water already present is $129600 \,cm^3$.The volume to be filled is $V_{fill} = 1980000 - 129600 = 1850400 \,cm^3$.Let $n$ be the number of bricks. The volume of one brick is $V_{brick} = 22.5 	imes 7.5 	imes 6.5 = 1096.875 \,cm^3$.Each brick absorbs $\frac{1}{17}$ of its volume,so the effective volume occupied by one brick in the water is $V_{eff} = V_{brick} - \frac{1}{17} V_{brick} = \frac{16}{17} V_{brick}$.To fill the cistern,the total volume of $n$ bricks must equal the volume to be filled: $n 	imes V_{eff} = V_{fill}$.$n 	imes \frac{16}{17} 	imes 1096.875 = 1850400$.$n 	imes \frac{16}{17} 	imes \frac{8775}{8} = 1850400$.$n 	imes \frac{2 	imes 8775}{17} = 1850400$.$n = \frac{1850400 	imes 17}{17550} = 1792$.

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