Question

A cuboidal box with dimension 3×3×2 cu. Units is melted into another cuboid whose width is 15 units . Find the length and height of the cuboidformed if l=h

Answer 1

Let's first find the volume of the original cuboidal box:

Volume = Length x Width x Height = 3 x 3 x 2 = 18 cubic units

We can then set up an equation to relate the volume of the original box to the volume of the new cuboid:

Volume of new cuboid = Volume of original box

Let's call the length and height of the new cuboid "x" (since we know that the length and height are the same). We know that the width of the new cuboid is 15 units. Therefore, we can write:

Volume of new cuboid = Length x Width x Height = x x 15 x x = 15x^2

Now we can set up the equation:

15x^2 = 18

Dividing both sides of the equation by 15 gives:

x^2 = 18/15

Simplifying the right side of the equation gives:

x^2 = 1.2

Taking the square root of both sides of the equation gives:

x ≈ 1.095

Therefore, the length and height of the new cuboid are approximately 1.095 units.