A well of diameter 8 metres is dug 18 metres deep. Earth taken out of it was spread evenly all around it in the shape of a circular ring of width 2 metres to form an embankment. If height of the embankment is ‘(h/5)’ metres, then how many statement(s) is/are false among the following statements?
I. Sum of each digit of ‘h’ is 9.
II. (h + 11) is a prime number.
III. Tenth digit of ‘h’ is smaller than its unit digit.
IV. Number of factors of ‘h’ is 12.

Solution

Inner radius of well = (8/2) = 4 metres Width of embankment = 2 metres So, outer radius of embankment = 4 + 2 = 6 metres Volume of cylindrical well = Volume of hollow embankment π X 4² X 18 = π X (6² - 4²) X height Or, 288 = 20 X height Or, height = (288/20) = (72/5) metres (h/5) = (72/5) Or, ‘h’ = 72 Statement I: Required sum = 7 + 2 = 9 So, statement I is true. Statement II: 72 + 11 = 83, which is prime So, statement II is true. Statement III: 7 < 2 So, statement III is false. Statement IV: 72 = 2³ X 3² Number of factors = (3 + 1) X (2 + 1) = 12 So, statement IV is true. Therefore, only one statement is false.