Question

A rectangular trough 8m long and 3m wide holds 57.6m^3 of water find the depth of water in the trough

Answer 1

Given,

Length of trough = 8 m
Wide of trough = 3 m

Then,

Let the Height of trough = h.

A/Q,

=> lbh = 57.6 m^3

=> 8 x 3 x h = 57.6 m^3

=> 24h = 57.6 m^3

=> h = (57.6/24) m

=> h = 2.4 m


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Answer 2

Given,

The length of a rectangular trough = 8 m

The breadth of the rectangular trough = 3 m

Amount/volume of water in the trough = 57.6 m^3

To find,

The depth of water in the trough.

Solution,

We can simply solve this mathematical problem using the following process:

Let us assume that the depth of water in the rectangular trough is x meters.

Mathematically, as per mensuration;

The volume of a cuboid

= length × breadth × depth

{Statement-1}

According to the question,

The water column in the rectangular trough is in the form of a cuboid whose base dimensions are that of the through and its height is equal to the depth of the water column present inside the trough.

=> volume of the cuboidal water column = 57.6 m^3

=> length × breadth × depth = 57.6 m^3

{according to statement-1}

=> 8 m × 3 m × x m = 57.6 m^3

=> x = 57.6/(8×3) m

=> x = 2.4 m

=> depth of water in the rectangular trough = 2.4 m

Hence, the depth of water in the rectangular trough is equal to 2.4 m.