Question : A solid cube has a side of 8 cm. It is cut along diagonals of the top face to get 4 equal parts. What is the total surface area (in cm2) of each part?
Option 1: $96 + 64\sqrt2$
Option 2: $80 + 64\sqrt2$
Option 3: $96 + 48\sqrt2$
Option 4: $80 + 48\sqrt2$
Correct Answer: $96 + 64\sqrt2$
Solution :
Diagonal of the face = (side of cube) × $\sqrt{2} = 8\sqrt{2}$ cm
The total surface area of the part
= Area of one face of cube + 2 × $\frac{1}{4}$ × area of top face + 2 × side of cube × $\frac{1}{2}$ × diagonal of face
= $8 × 8 + \frac{1}{2} × 64 + 2 × 8 × \frac{1}{2} × 8\sqrt2$
= $64 + 32 + 64\sqrt2$
= $96 + 64\sqrt2$ cm
2
Hence, the correct answer is $96 + 64\sqrt2$.
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