Question

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 1

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.

Answer 2

Glance at the given steps:-

Given that,

• Diagonal of the cuboid = 10 cm

⇒ $\it \sqrt{l^2 + b^2 + h^2} = 10 \ cm$

• Sum of length, breadth and height = 80 cm

⇒ $\it l + b + h = 80 \ cm$.

We have already studied that,

$\it (a + b + c)^2 = a^2 + b^2 + c^2 + 2(ab + bc + ca)$

We can also rewrite it as,

$\it (sum)^2 = (diagonal)^2 + TSA$

⇒ $\it x = (80)^2 - (10)^2$

(assume TSA = x)

⇒ $\it x = 6300$.

Or, TSA is equal to $\it 6300$ cm².