## 2) In a courtyard, 1.4 metre diameter and 10 mdeep well was dug. The excavated soil wasspread on the cuboid shape of c

Question

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

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4 months 2021-08-01T09:29:21+00:00 2 Answers 0 views 0

1. 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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in a solid hemisphere the circumference of circular base

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2. 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) .