2) In a courtyard, 1.4 metre diameter and 10 m
deep well was dug. The excavated soil was
spread on the cuboid shape of courtyard. The
length and width of the courtyard is 55 metre
and 14 metre respectively. So find the
thickness of that spread soil.
Answers
Given : In a courtyard, 1.4 metre diameter and 10 m deep well was dug. The excavated soil was spread on the cuboid shape of courtyard. The
length and width of the courtyard is 55 metre and 14 metre respectively.
To find : the thickness of that spread soil.
Solution:
1.4 metre diameter and 10 m deep well was dug.
Volume of soil extracted = πR²h
R = 1.4/2 = 0.7
h = 10 m
π = 22/7
=> Volume of soil extracted = (22/7) * (0.7)² * 10
= 22 * 0.1 * 0.7 * 10
= 15.4 m³
Volume of cuboid = 55 x 14 x thickness
55 x 14 x thickness = 15.4
=> 55 x thickness = 1.1
=> thickness = 1.1/55 m
=> thickness = 110/55 cm
=> thickness = 2 cm
thickness of that spread soil. = 2 cm
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Solution :-
Let us assume that, the thickness of that spread soil is x m .
so,
→ Volume of soil dug out = Volume of courtyard in the shape of cuboid .
we know that,
- Volume of cylinder = π * (radius)² * height(depth) .
- Volume of cuboid = Length * Breadth * height(thickness) .
- Radius = Diameter / 2 .
putting given values we get,
→ (22/7) * (1.4/2)² * 10 = 55 * 14 * x
→ (22/7) * (0.7)² * 10 = 55 * 14 * x
→ 22 * 0.1 * 0.7 * 10 = 55 * 14 * x
→ 2.2 * 7 = 55 * 14 * x
→ 2.2 = 55 * 2 * x
→ 110x = 2.2
→ x = (22/1100)
→ x = (2/100)
→ x = 0.02 m or 2 cm. (Ans.)
Hence, the thickness of that spread soil is 0.02 m (2cm) .
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