Question

Total surface area of a cuboid is 22m2. If its length is 2m and height
is 3m, find the breadth and the volume.​

Answer 1

Answer :

Breadth of the cuboid is 1 m and volume of the cuboid 6 m³

Step by step Explanatíon

We have ,

• Length of cuboid, l = 2m
• Height of cuboid , h = 3m
• Total surface area of a cuboid , S = 22m²

We have to find the breath of the cuboid and volume of the cuboid .

We know that ,

Total surface area of a cuboid

$\sf\:S=2(lb+bh+hl)$

$\sf\implies22=2(2b+3b+2\times3)$

$\sf\implies11=2b+3b+6$

$\sf\implies11-6=5b$

$\sf\implies5=5b$

$\sf\implies\:b=\dfrac{5}{5}$

$\sf\implies\:b=1m$

Now,

Volume of Cuboid

$\sf\:V=l\:\times\:b\:\times\:h$

$\sf\implies\:V=2\times3\times1$

$\sf\implies\:V=6m^3$

Answer 2

Answer:

Given :-

• Total surface area of a cuboid is 22 m².
• Length of a cuboid is 2 m and height is 3m.

To Find :-

• What is the breadth and volume.

Solution :-

Given :

• Total surface area = 22 m²
• Length = 2 m
• Height = 3 m

To find breadth we know that,

$\leadsto$ Total Surface Area = 2(lb + bh + hl)

=> 22 = 2{(2b) + (3b) + (3 × 2)}

=> $\sf\dfrac{\cancel{22}}{\cancel{2}}$ = (2b + 3b + 6)

=> 11 = 2b + 3b + 6

=> 11 = 5b + 6

=> - 5b = 6 - 11

=> - 5b = - 5

=> b = $\sf\dfrac{\cancel{- 5}}{\cancel{- 5}}$

$\implies$ b = 1 m

Now, we have to find the value of volume,

$\leadsto$ Volume = Length × Breadth × Height

=> Volume = 2 × 3 × 1

$\implies$ Volume = 6 m³

Hence, the breadth is 1 m and the volume is 6m³ .