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A tank 9 m long, 4 m wide, and (1/3) m deep is dug in a field 24 m long and 14 m wide. If the dug soil is spread evenly over the rest of the field, then by how much will the height of the field increase?

A tank 9 m long, 4 m wide, and (1/3) m deep is dug in a field 24 m long and 14 m wide. If the dug soil is spread evenly over the rest of the field, then by how much will the height of the field increase? Correct Answer 4 cm

Given:

Length of tank = 9 m

Width of tank = 4 m

Height of tank = 1/3 m 

Length and breadth of the field are 24 m and 14 m respectively.

Formula used:

The volume of cuboid = Length × Breadth × Height

Area of Rectangle = Length × Breadth

Calculation:

Let the height of the field increased be x m 

According to the question,

Area of the field where the mud will be spread = 24 × 14 - 9 × 4 = 300 m2

The volume of earth taken out = the volume of the mud spread over the field

⇒ 9 × 4 × 1/3 = 300 × y 

Increase height = (12/300) = 0.04 m = 4 cm

∴ The height of the field increased by 4 cm.

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