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Earth is dug out in a cylindrical shape from a plot of land. The hole is $30 m$ deep and $7 m$ in diameter. This earth is spread out on an adjacent plot of land, which is in the shape of a rectangle of length $33 m$ and breadth $14 m$ . To what extent will the height of the rectangular plot rise?

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1.5 m

3.5 m

2.0 m

2.5 m

answer is D.

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Detailed Solution

We have, length of cylinder

(l) = 30 m

Diameter of the cylinder

(d) = 7 m

Radius of the cylinder

(r) = \frac{d}{2} = \frac{7}{2} m

Now,
Volume of cylinder

V = π r^{2} h

V = \frac{22}{7} \times (\frac{7}{2})^{2} \times 30

V = \frac{22}{7} \times \frac{7}{2} \times \frac{7}{2} \times 30

V = 11 \times 7 \times 15

V = 1155 m^{3}

— (|)
A/Q This volume is spread into a rectangle.
So,

Volume of cylinder = Volume of rectangle

Volume of rectangle

= l \times b \times h

— (||)
From (|) and (||),

1155 = 33 \times 14 \times h (∵ l = 33 m, b = 14 m)

h = \frac{1155}{33 \times 14}

h = 2.5 m

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