NCHMCT JEE 2021 Question Paper with solutions for online practice

Question : 62 of 200

Marks: +1, -0

A well of diameter

3 {m}

is dug

14 {m}

deep. The Earth taken out of it has been spread evenly all around it in the shape of a circular ring of width

4 {m}

to form an embankment.
Find the height of the embankment.

Solution:

(d) Let, height of embankment

=h {m}

Given, radius of well

=\;{3}/{2}=1.5 {m}

According to the question,

\;{4}/{3} × \;{22}/{7} ×[(4)^{2}-(1.5)^{2}] × h=\;{22}/{7} ×(1.5)^{2} × 14

⇒ \;\; \;{4}/{3} ×(16-2.25) × h=2.25 × 14

⇒ \;\; \;{4}/{3} × 13.75 × h=2.25 × 14

⇒ \;\; \;{4}/{3} ×(16-2.25) × h=2.25 × 14

⇒ \;\; \;{4}/{3} × 13.75 × h=2.25 × 14

⇒ \;\; h=\;{2.25 × 14 × 3}/{4 × 13.75}

⇒ h=\;{225 × 7 × 3}/{2 × 1375}

⇒ h=\;{189}/{110}=1.718 ≈ 1.75

∴ \;h=1.75 {m}

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