The sum of the length, width and depth of a cuboid is 8 cm and its diagonal is 5 cm. What is its surface area?

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  1. 39 cm2
  2. 64 cm2
  3. 25 cm2
  4. 89 cm2

Answer (Detailed Solution Below)

Option 1 : 39 cm2
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Detailed Solution

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Given:

Length + Width + Height = 8 cm

Diagonal = 5 cm

Formula used:

Diagonal2 = l2 + w2 + h2

Surface Area = 2 × (lw + wh + hl)

Calculation:

Let l + w + h = 8 ...(i)

⇒ Diagonal2 = 52 = 25

⇒ l2 + w2 + h2 = 25 ...(ii)

Now, (l + w + h)2 = l2 + w2 + h2 + 2(lw + wh + hl)

⇒ 82 = 25 + 2(lw + wh + hl)

⇒ 64 = 25 + 2(lw + wh + hl)

⇒ 2(lw + wh + hl) = 39

⇒ lw + wh + hl = 19.5

Surface Area = 2 × 19.5 = 39 cm2

∴ The surface area is 39 cm².

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