Question

A metal rod 25 cm, 20 cm, 16 cm is melted to form a cube. The length of the cube is ______.

पर्याय

• 20 cm

• 15 cm

• 8 cm

• 10 cm

Answer 1

A metal rod 25 cm, 20 cm, 16 cm is melted to form a cube. The length of the cube is 20 cm.

Explanation:

We are given a metal rod with dimensions 25 cm × 20 cm × 16 cm and it is melted to form a cube. We are asked to find the length of the cube.

Step 1: Find the volume of the metal rod

The volume V of the metal rod is calculated using the formula for the volume of a rectangular prism:

V = length × width × height

Substitute the given dimensions:

V = 25 × 20 × 16 = 8000 cm³

Step 2: Volume of the cube

The volume of the cube is the same as the volume of the rod because the rod is melted to form the cube.

The volume V of a cube is given by:

V = side³

Let the side length of the cube be s. Thus, we have:

s³ = 8000

Step 3: Solve for s

To find s, take the cube root of both sides:

`s = root(3)(8000) = 20` cm