Sainik School Entrance Exam 2020 Solved Paper

Question : 45 of 150

Marks: +1, -0

Some cubic metres of earth is dug out to sink a well which is

16 {\m}

deep and which has a radius of

3.5 {\m}

. If that amount of earth when taken out is spread over a rectangular plot of dimensions

25 {\m} × 16 {\m}

, what is the height of the platforms so formed?

Solution:

(a) Well's depth

=h=16 {\m}, {\r}=3.5 {\m}={7}/{2} {\m}

∴ Volume of a well (cylinder)

=πr^2 h

={22}/{7} ×({7}/{2})^2 ×16 {\m}^3

Now, amount of earth

=

Volume of a well = Volume of a rectangular platform

∴ 25 {\m} ×16 {\m} ×h={22}/{7} ×({7}/{2})^2 ×16 {\m}^3

⇒ h={22}/{7} ×{7}/{2} ×{7}/{2} ×{1}/{25}={77}/{50} {\m}=1.54 {\m}

So, the height of the platform

=h=1.54 {\m}

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