A cuboidal vessel is 10 m long and 8 m wide. How high must it be made to hold 380 cubic metres of a liquid?

Solution:

Given: Length and breadth of the cuboidal vessel are 10 m and 8 m respectively. It must hold 380 m³ of a liquid.

Since the vessel is cuboidal in shape, the volume of liquid in the vessel will be equal to the volume of the cuboid.

The volume of the cuboid of length l, breadth b, and height h, is V = l × b × h

Let the height of the cuboidal vessel be h.

Length of the cuboidal vessel, l = 10 m

The breadth of the cuboidal vessel, b = 8 m

The capacity of the cuboidal vessel (V) = 380 m³

Volume of the liquid in the cuboidal vessel = l × b × h

l × b × h = 380m³

10 m × 8 m × h = 380m³

h = 380 / (10 × 8)

h = 4.75 m

Thus, the cuboidal vessel must be made 4.75 m high.

☛ Check: NCERT Solutions for Class 9 Maths Chapter 13

Video Solution:

A cuboidal vessel is 10 m long and 8 m wide. How high must it be made to hold 380 cubic metres of a liquid?

Class 9 Maths NCERT Solutions Chapter 13 Exercise 13.5 Question 3

Summary:

It is given that there is a cuboidal vessel that is 10 m long and 8 m wide that can hold 380 cubic metres of liquid. We have found that the cuboidal vessel must be made 4.75 m high.

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