Question

The length and the breadth of a cuboid are 14 cm and 6 cm, respectively. Find the height of the cuboid if the volume of the cuboid is 756 cm³. ​

Answer 1

Given:-

• Length(l) =14cm
• breadth(b) =6cm
• volume=756cm³
• height(h) =?

Solution:-

Volume of cuboid=l×b×h

756=14×6×h

756=84×h

h=756÷84

h=9cm

So, the height of cuboid is 9cm

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Answer 2

Explanation -:

Given :

• Length of a cuboid = 14 cm
• Breadth of a cuboid = 6 cm
• Volume of a cuboid = 756 cm³

To Find :

• Height of the cuboid

Solution :

Let us assume the height as 'x'

$\large \boxed{ \rm{ Volume \: of \: a \: cuboid  = Length × Breadth × Height }}$

$\small\rm\bf{14 \times 6 \times x = 756}$

$⤍ \small\rm{84 \times x = 756}$

$⤍ \small\rm{84x = 756}$

$⤍ \small\rm{x = \cancel\frac{756}{84} = 9 }$

$\small\fbox { \rm{x = 9cm}}$

CHECK :

Volume of a cuboid = length × breadth × height

→ 14 × 6 × 9 cm

→ 756 cm³

Hence, proved

$\rule{70mm}{2pt}$

$\large\fbox{ \fbox{ \rm{Additional information}}}$

$• \: \small\rm{Perimeter \: of \: a \: cuboid = 4(length + breadth + height)}$

$• \: \small\rm{Diagonal \: of \: a \: cuboid = \sqrt{ ( {length}^{2} + {breadth}^{2} + {height}^{2} }}$

$• \: \small\rm{Total \: Surface \: Area \: of \: a \: Cuboid = 2 (lb + bh + lh)}$

$• \: \small\rm{Total \: surface \: area \: of \: a \: cube = 6( {side)}^{2}}$

$• \: \small\rm{ Volume \: of \: a \: cube = {side}^{3} }$

$\rule{70mm}{2pt}$

✯ NOTE :

L = Length

B = Breadth

H = Height