Question
Download Solution PDFThe sum of the length, width and depth of a cuboid is 8 cm and its diagonal is 5 cm. What is its surface area?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
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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