Question

Question :3
The ratio of length, breadth and height of a cuboid is 5:2:4,
respectively. The volume of the cuboid is 13720cm3. If each
edge of a cube is 1/7th of the sum of the length, breadth and
height of the cuboid, then find the total surface area of the
cube.​

Answer 1

Answer:

726 cm²

Step-by-step explanation:

Let the dimensions be 5x, 2x and 4x

We know,

Volume of a cuboid = lbh

ATQ,

$(5x)(2x)(4x) = 13720\\40 x^3 = 13720\\x^3 = 343\\x = 7 cm\\So,\\l = 5x = (5)(7) = 35 cm\\b = 2x = (2)(7) = 14 cm\\h = 4x = (4)(7) = 28 cm\\Edge(cube) = a\\So, \\ATQ,\\1/7(l + b +h)\\= 1/7(35 + 14 + 28)\\= 1/7(77)\\= 11 cm$

Now, edge of cube = 11 cm

$So,\\TSA(cube) = 6a^2\\= 6(11)(11)\\= (66)(11)\\= 726 cm^2$