Question

2. The length, breadth and height of a cuboid are in the ratio 6:4:7. If total surface area of the cuboid is given as 1692 cm², find its volume. ​

Answer 1

Answer: 4536 cm3

Step-by-step explanation:

Given ratio of length, breadth and height of a cuboid is 6:4:7

Let the length of a cuboid (l) = 6x

breadth of a cuboid (b) = 4x

height of a cuboid (h) = 7x

Given surface area of cuboid = 1692 cm²

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

So,

2{(6x)(4x) + (4x)(7x) + (7x)(6x)} = 1692 cm²

2(24x²+ 28x² + 42x²) = 1692 cm²

2(94x²) = 1692 cm²

94x² = 846 cm²

x² = 9 cm²

x = 3 cm

Thus, length = 6x = 18 cm , breadth = 4x = 12 cm , height = 7x = 21 cm

Now,

Volume of cuboid =  l * b * h

Volume of cuboid =  (18cm)(12cm)(21cm) = 4536 cm3