Question

A field is a field is 30 M long and 18 metre broad .A pit 6 m long,4 m wide and 3 M deep is dug out from the middle of the field and the earth removed is evenly spread over the remaining area of the field find the rise in the level of the remaining part of the field in centimetres correct to 2 decimal places

Answer 1

Final Answer:

After a pit 6 m long, 4 m wide and 3 metre deep is dug out from the middle of the field 30 metre long and 18 metre broad and the earth removed is evenly spread over the remaining area of the field, the rise in the level of the remaining part of the field in centimetre correct to 2 decimal places is 13.95 centimetre.

Given:

A field is 30 metre long and 18 metre broad.

A pit 6 m long, 4 m wide and 3 metre deep is dug out from the middle of the field and the earth removed is evenly spread over the remaining area of the field.

To Find:

The rise in the level of the remaining part of the field in centimetre correct to 2 decimal places.

Explanation:

The area $A$ of the rectangle with the length $l$ metre and the breadth $b$ metre is $A=l\times b$.

The volume $V$ of the rectangle with the length $l$ metre, the breadth $b$ metre  and the height $h$ metre is $V=l\times b \times h$.

Step 1 of 5

The area of the field is 30metre long and 18metre broad is equal to the area of the rectangle with the length 30metre and the breadth 18metre, which is calculated to be

$=30\times 18\\=540metre^2$

Step 2 of 5

The area of the pit 6metre long, 4metre wide and 3metre deep is equal to the area of the rectangle with the length 6metre and the breadth 4metre, which is calculated to be

$=6\times 4\\=24metre^2$

Step 3 of 5

The volume of the pit 6metre long, 4metre wide and 3metre deep is equal to the volume of the rectangle with the length 6metre, the breadth 4metre and the height 3metre, which is calculated to be

$=6\times 4\times 3\\=72metre^3$

This is the measure of the   earth removed from the referred pit.

Step 4 of 5

The earth removed is evenly spread over the remaining area of the field. So the remaining area of the field is

$=540metre^2-24metre^2\\=516metre^2$

Assume that the rise in the level of the remaining part of the field is $h$ metre.

Step 5 of 5

Taking the above data into consideration, write the following equation.

$72meter^3=(516\times h) metre^3\\h=\frac{72}{516} metre\\h=\frac{72\times 100}{516} centimetre\\h \approx 13.95 centimetre$

Therefore, after a pit 6 m long, 4 m wide and 3 metre deep has been dug out from the middle of the field 30 metre long and 18 metre broad and the dug-out earth is evenly spread over the remaining area of the field, the required rise in the level of the remaining part of the field in centimetre correct to 2 decimal places is 13.95 centimetre.

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Answer 2

Answer:

The rise in the level of the remaining part of the field is 13.9 cm, rounded to 2 decimal places.

Step-by-step explanation:

From the above question,

They have given :

The volume of earth removed from the pit can be calculated as follows:

                  Volume = Length * Width * Depth

                                = 6 m * 4 m * 3 m

                                 = 72 $m^{3}$

The remaining area of the field can be calculated as follows:

                      Area = Length * Width

                                = 30 m * 18 m

                                = 540 $m^{2}$

Subtracting the area of the pit from the total area of the field gives us the remaining area:

   Remaining Area = 540 $m^{2}$ - (6 m * 4 m)

                                = 540 $m^{2}$ - 24  $m^{2}$

                                = 516 $m^{2}$

To find the rise in the level of the remaining part of the field, we need to calculate the average height to which the earth removed from the pit was spread:

            Average Height = Volume / Remaining Area

                                        = 72 $m^{3}$ / 516  $m^{2}$

                                        = 0.139 m

                                        = 13.9 cm

So, the rise in the level of the remaining part of the field is 13.9 cm, rounded to 2 decimal places.

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