The length of diagonal of a cuboid is 10cm and sum of its length,bread

1.	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???
Answer» 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 ⠀⠀━━━━━━━━━━━━━━━━━━━⠀ « 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 ⠀⠀━━━━━━━━━━━━━━━━━━━⠀ Formula of total surface area is 2 (lb + bh + hl) . ∴ Hence, Total surface area of the cuboid is 6300cm.

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???

Answer»

Given:

To find:

Solution:

• Let's consider l + b + h = 80 …(i) as equation (i).

Where,

⠀⠀━━━━━━━━━━━━━━━━━━━⠀

« 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

⠀⠀━━━━━━━━━━━━━━━━━━━⠀

∴ Hence, Total surface area of the cuboid is 6300cm.