Question

एक घनाभ की लंबाई चौड़ाई और ऊंचाई का योग 19 सेंटीमीटर है तथा विक्रम की लंबाई 11 सेंटीमीटर है घन का पृष्ठीय क्षेत्रफल ज्ञात कीजिए​

Answer 1

Given:

The sum of length breadth and depth of a cuboid is 19 cm and the length of diagonal is 11 centimetres

To find:

The surface area of a cuboid.

Solution:

The sum of length, breadth & height of the cuboid is 19 cm

i.e., l + b + h = 19

The diagonal "d" of the cuboid is,

$\sqrt{l^2 + b^2 + h^2 } = 11$

squaring on both sides

$\implies \bold{l^2 + b^2 + h^2 = 121}$

We know an identity as:

(a + b + c)² = a² + b² + c² + 2(ab+ bc + ca)

∴ (l + b + h)² = l² + b² + h² + 2(lb+ bh + hl)

⇒ 19² = 121 + 2(lb+ bh + hl)

⇒ 361 - 121 = 2(lb+ bh + hl)

⇒ 2(lb+ bh + hl) = 240

since the surafec area of the cuboid is 2(lb+ bh + hl)

⇒ Surface area of the cuboid = 240 cm²

Thus, the surface area of a cuboid is → 240 cm².

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