Question 57

A plot of land in the form of a rectangle has a dimension 240 m × 180 m. A drainlet 10m wide is dug all around it (outside) and the earth dug out is evenly spread over the plot, increasing its surface level by 25 cm. The depth of the drainlet is

Solution

Volume of the plot = 240 m x 180 m x 0.25 m = 10800 m$$^{3}$$

($$\because$$ The earth dug out is evenly spread over the plot, increasing its surface level by 25 cm)

Total volume of the drainlet is given by,

= (2 x 260 x 10 x h) + (2 x 180 x 10 x h) m$$^{3}$$

Volume of the plot is equal to the volume of the drainlet,

10800 m$$^{3}$$ = (2 x 260 x 10 x h) + (2 x 180 x 10 x h) m$$^{3}$$

10800 = h(5200 + 3600)

10800 =  h(8800)

h = 1.227

Hence, option C is the correct answer.


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