A cube or a cuboid had the volume the measurement of the cubiod area in the ratio 1:2:3

if the difference between thee cost of painting the cuboid & cube (whole surface area) at the rate of 5m is rs80 find their volume

To find the volume of the cube or cuboid, we need to determine the ratio of their side lengths. Let's assume the side lengths to be x, 2x, and 3x.

The surface area of a cube is given by 6x^2, where x is the side length.
The surface area of a cuboid is given by 2(2x * 3x + 3x * x + 2x * x) = 2(6x^2 + 5x^2 + 4x^2) = 2(15x^2) = 30x^2.

Given that the cost difference of painting the cuboid and cube is Rs80, and the rate of painting is Rs5 per square meter, we can set up the following equation:

30x^2 * 5 - 6x^2 * 5 = 80.

Simplifying the equation, we have:

150x^2 - 30x^2 = 80,
120x^2 = 80,
x^2 = 80/120,
x^2 = 2/3.

Taking the square root of both sides, we get:

x = √(2/3).

Therefore, the side lengths of the cube or cuboid are x = √(2/3), 2x = 2√(2/3), and 3x = 3√(2/3).

The volume of the cube is (x)^3 = (√(2/3))^3 = 2√2/3.

The volume of the cuboid is (2x)(3x)(x) = (2√(2/3))(3√(2/3))(√(2/3)) = 6√2/3 * 2/3√2 * √2/3 = 48/27.

Therefore, the volume of the cube is 2√2/3 and the volume of the cuboid is 48/27.