Math, asked by abhay3149, 2 months ago

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 Anonymous
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 Anonymous
6

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.

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