The length of diagonal of a cuboid is 10cm and sum of its length,breadth,and height is80 cm. Find the total surface area of the cuboid.
answer is 6300 m but why???
Answers
Answered by
40
Given:
- Diagonal of a cuboid = 10cm
- Sum of its length,breadth,and height = 80 cm
To find:
- The total surface area of the cuboid.?
Solution:
• Let's consider l + b + h = 80 …(i) as equation (i).
Where,
- Hypotenuse = Diagonal = 10cm
- Base = Length
- Perpendicular = Height
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« Now, By using Pythagoras Theorem,
√l² + b² + h² = (10)²
→ l² + b² + h² = 100 ...(ii)
Using ...(i), l + b + h = 80
« On squaring both sides, we have,
l + b + h = 80
→ (l + b + h)² = (80)²
→ l² + b² + h² + 2 (lb + bh + hl) = 6400
→ 100 + 2 (lb + bh + hl) = 6400
→ 2 (lb + bh + hl) = 6400 - 100
→ 2 (lb + bh + hl) = 6300
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- Formula of total surface area is 2 (lb + bh + hl) .
∴ Hence, Total surface area of the cuboid is 6300cm.
Answered by
6
Glance at the given steps:-
Given that,
- Diagonal of the cuboid = 10 cm
⇒
- Sum of length, breadth and height = 80 cm
⇒ .
We have already studied that,
We can also rewrite it as,
⇒
(assume TSA = x)
⇒ .
Or, TSA is equal to cm².
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