Question

A vessel in the shape of a cuboid is 30cm long and 25cm wide. What should be it's height to hold 4.5 liters of water?​

Answer 1

Answer:

The Height of the cuboid should be 6 cm.

Step-by-step explanation:

Given :

Length = 30 cm

Breadth = 25 cm

Water supposed to be hold = 4.5 l

To find :

The height of the cuboid

Solution :

Convert all the quantities into same units.

★ Conversion of 4.5 litres into cubic centimetres -

$\boxed{\sf{1\:Litre=1000\:Cubic\: Centimetres}}$

$\sf{\implies} \: 4.5 \times 1000 \\ \\ \sf{\implies} \:4500 \: {cm}^{3}$

The required capacity of the cuboid is 4500 cm³.

$\rule{300}{1.5}$

★ Height of the cuboid -

Let the Height be h

The capacity required is the volume of the cuboid.

$\boxed{\sf{Volume=Length \times Breadth \times Height}}$

$\sf{\implies} \:30 \times 25 \times h = 4500 \\ \\ \sf{\implies} \:750h = 4500 \\ \\ \sf{\implies} \:h = \dfrac{450\cancel{0}}{75\cancel{0}} \\ \\ \sf{\implies} \:h = 6$

Height = 6 cm

$\therefore$ The Height of the cuboid should be 6 cm.

Answer 2

Answer:

$\bold\green{Height\:of\:cuboid}$ = $\bold{6\:cm}$

Step-by-step explanation:

Given:-

• Length of cuboid = 30 cm
• Width of cuboid = 25 cm
• Capacity = 4.5 l
• Height of cuboid = ?

We know that,

$\bigstar {\boxed{\bold{1\:liter= 1000\:{cm}^{3} }}}$

$\Rightarrow\sf Capacity = (4.5 \times 1000)\:{cm}^{3} \\\\\Rightarrow{\boxed{\sf\red{Capacity = 4500\:{cm}^{3}}}}$

$\therefore\bold{Volume\:of\:cuboid=4500\:{cm}^{3} }$

$\rule{300}{1}$

We know that,

$\bigstar{\boxed{\bold{Volume\:of\:cuboid=Length \times Breadth \times Height }}}$

$\sf \: *\: Substituting\:values:-$

$\Rightarrow\sf 4500 = 30\times 25\times Height \\\\\Rightarrow\sf 4500 = 750 \times Height \\\\\Rightarrow\sf Height =\cancel{\dfrac{4500}{750} } \\\\\Rightarrow{\boxed{\bold\red{Height = 6\:cm}}}$

$\therefore\bold{Height\:should\:be\:6\:cm}$