Question

A cuboid of size 50 cm × 40 cm × 30 cm is cut into 8 identical parts by 3 cuts. what is the total surface area (in cm2) of all the 8 parts?

Answer 1

A Cuboid of dimensions 30 × 50 × 40 is divided into 8 part by cutting 3 times .
It means each dimension { e.g., Length Breadth and height} cut in two equal parts as shown in figure .

I mean after cutting each new Cuboid will be 15 × 25 × 20
Let Length = 25 , Breadth = 20 and height = 15 of each Cuboid .

We know, the formula,
total surface of Cuboid = 2[ L × B + B × H + H × L ]

so, total surface area of each Cuboid = 2[ 25 × 20 + 20 × 15 + 15 × 25 ]
= 2 [ 500 + 300 + 375 ]
= 2 [ 1175 ] = 2350 square unit

hence, Total surface area of each part = 2350 square unit

Total surface area of all the eight parts = 2350 × 8 = 18800 square unit

Answer 2

Hello Dear.

Here is your answer---

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As per as the Question,

Measurement of the Cuboids = 50 cm × 40 cm × 30 cm.
        Thus, Length = 50 cm.
               Breadth = 40 cm.
                Height = 30 cm.


If the Cuboid will be cut into eight equals parts by three cuts, then Length, Breadth and the Height of the each part formed by the Cutting of the Cuboid will become Half of the Original length, Breadth and Height of the Original Cuboid.


Thus, 
    For each single Cuboid,
 
Length(l) = 50/2
               = 25 cm.

Breadth(b) = 40/2
                   = 20 cm.

Height(h) = 30/2
                =  15 cm.

For the Total Surface area of the Single cut cuboid,

Using the Formula,
   Total Surface Area of the Cuboid = 2[lb + bh + hl]
            ∵ T.S.A. = 2[ 25 × 20 + 20 × 15 + 15 × 25]
          ⇒ T.S.A. = 2[ 500 + 300 + 375]
               T.S.A. = 1175 cm²

Thus, the total surface area of the each single cuboid formed by the cutting the original Cuboid is 1175 cm².


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