Question

200
7. A trench 5 m long and 2 m wide is dug 1.5 m
deep. The soil from this is spread evenly on a
patch of ground 15 m long and 1.25 m broad.
What is the height of the soil spread over
the patch?​

Answer 1

Required Answer:

We have:-

• The dimension of the trench is 5 m long and 2 m wide is dug 1.5 m deep.
• The soil from this is spread evenly on a
• patch of ground 15 m long and 1.25 m broad$.$

To FinD:-

• Height of the soil spread over the patch?

Step-by-Step Explanation:

The trench is in the shape of a cuboid. Hence, the volume of soil taken out would be the volume of the cuboid of same dimension.

The volume of soil taken out = Volume of soil spread over the patch. It means, volume of the trench = Volume of the rectangular patch.

Volume of the trench:

= L × B × H

= 5 m × 2 m × 1.5 m

= 15 m³

According to relation:

• Volume of trench = Volume of patch

⇒ l × b × h = 15 m³

⇒ 15 m × 1.25 m × h = 15 m³

⇒ h = 1 / 1.25 m

⇒ h = 0.8 m

Hence:-

• The height of the soil spread over the patch is 0.8 m or 80 cm

Answer 2

Given:-

• A trench is 5 m long.

• A trench is 2 m wide.

• The trench had dug 1.5 m deep.

• The ground is 15 m long.

• The ground is 1.25 m broad.

To Prove:-

• Height of the soil spread over the patch.

Solution:

• Volume of trench = L × B × H

• Volume of trench = 5 × 2 × 1.5

• Volume of trench = 15 m³

As we know that..

• Volume of patch = Volume of trench.

• 15 × 1.25 × height = 15

• height = 1 / 1.25 ( by canceling 15)

• height = 0.8 m or 80 cm..

$\:$

Hence the height of the soil spread over trench is 0.8 m or 80cm