The sides of a cuboid are in the ratio 3 : 4 : 5 and its surface area is equal to the surface area of the cube with side 6 units. What is the approximate volume of the cuboid?

Solution / समाधान :

Let sides of cuboid be $3x, 4x, 5x$

Surface area of cuboid = $2(lb + bh + hl)$
$= 2(3x \cdot 4x + 4x \cdot 5x + 5x \cdot 3x)$
$= 2(12x^2 + 20x^2 + 15x^2)$
$= 2(47x^2) = 94x^2$

Surface area of cube (side = 6):
$= 6 \times 6^2 = 216$

Equate:
$94x^2 = 216$
$x^2 \approx 2.3 \Rightarrow x \approx 1.52$

Volume of cuboid:
$= 3x \cdot 4x \cdot 5x = 60x^3$

$x^3 \approx 1.52^3 \approx 3.5$

Volume $\approx 60 \times 3.5 = 210$
Final Answer / अंतिम उत्तर: 210