The length, breadth and height of a cuboid are in the ratio 3 : 4 : 6

1.	The length, breadth and height of a cuboid are in the ratio 3 : 4 : 6 and its volume is 576 cm3. The whole surface area of the cuboid is A. 216 cm2 B. 324 cm2 C. 432 cm2 D. 460 cm2
Answer» We know that, Volume of cuboid = Length × Breadth × Height 576 = 3x × 4x × 6x 576 = 72x³ x = \(\sqrt[3]{\frac{576}{72}}\) = 2 Therefore, Total surface area of cuboid = 2 (lb + bh + hl) = 2 (3x × 4x + 4x × 6x + 6x × 3x) = 2 (48 + 96 + 72) = 432 cm²

The length, breadth and height of a cuboid are in the ratio 3 : 4 : 6 and its volume is 576 cm3. The whole surface area of the cuboid is A. 216 cm2 B. 324 cm2 C. 432 cm2 D. 460 cm2

Answer»

We know that,

Volume of cuboid = Length × Breadth × Height

576 = 3x × 4x × 6x

576 = 72x³

x = \(\sqrt[3]{\frac{576}{72}}\)

= 2

Therefore,

Total surface area of cuboid = 2 (lb + bh + hl)

= 2 (3x × 4x + 4x × 6x + 6x × 3x)

= 2 (48 + 96 + 72)

= 432 cm²