Question

The capacity of the cuboidal shaped vessel of length 80 cm and breadth 60 cm is 192 litres .What is it's height​

Answer 1

Answer:

• Height of the cuboidal vessel is 40 cm.

Step-by-step explanation:

Given that:

• The capacity of a cuboidal shaped vessel is 192 litres.
• The length of the vessel is 80 cm.
• The breadth of the vessel is 60 cm.

To Find:

• Height of the vessel.

Solution:

Converting 80 cm and 60 cm to m:

As we know that,

• 1 cm = 100 m

Therefore,

80 cm = (80/100) m = 0.8 m

60 cm = (60/100) m = 0.6 m

Finding volume of the cuboidal vessel:

As we know that:

• Volume of a cuboid = (l × b × h) cubic units

Where,

• l = Length of the cuboid

• b = Breadth of the cuboid

• h = Height of the cuboid

Let us assume,

• Height be h.

Then,

Volume of the cuboidal vessel = l × b × h

Substituting the values,

$\sf\hookrightarrow 80cm\times60cm\times h$

Taking 80 cm and 60 cm in metre,

$\sf\hookrightarrow 0.8\times0.6\times h$

Multiplying the numbers,

$\sf\hookrightarrow 0.48h$

Finding the capacity of water the vessel can hold:

As we know that:

• 1 m³ = 1000 litres

Therefore,

Capacity of water the vessel can hold = 0.48h × 1000

= 480h

Finding the height of the vessel:

According to the question,

$\sf{\hookrightarrow 480h = 192}$

Transposing 480 from LHS to RHS and changing its sign,

$\sf{\hookrightarrow h = \dfrac{192}{480}}$

Dividing 192 by 480,

$\sf{\hookrightarrow h = 0.4}$

Hence, height of the vessel is 0.4 m = (0.4 × 100)cm = 40 cm

Verification:

Converting all the dimensions in m,

• 80 cm = 0.8 m
• 60 cm = 0.6 m
• 40 cm = 0.4 m

LHS:

$\sf\hookrightarrow (0.8\times0.6\times 0.4)\times1000\\\\\hookrightarrow 0.192\times1000\\\\\hookrightarrow 192$

RHS:

$\sf\hookrightarrow 192$

LHS = RHS

Hence, Verified