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,

$(5x)(2x)(4x)=13720 cm^3\\40x^3=13720\\x^3 = 343\\x = 7cm\\So,\\l = 5x = (5)(7) = 35 cm\\b = 2x = (2)(7) = 17 cm\\h = 4x = (4)(7) = 28 cm\\edge(cube) = a\\so,\\ATQ,\\a = 1/7 (l +b+h)\\= 1/7(35 + 17 + 28)cm\\= 1/7 (77)\\= 11 cm\\TSA(cube) = 6a^2\\= (6)(11)(11)\\= (66)(11)\\=726 cm^2$