Question

Two metal rods of dimensions are 5 cm by 8 cm by 3 cm and 8 cm, 6 cm, 2 cm are melted and formed into a cube. The side of the cube is ______.

पर्याय

• 4 cm

• 5 cm

• 6 cm

• 8 cm

Answer 1

Two metal rods of dimensions are 5 cm by 8 cm by 3 cm and 8 cm, 6 cm, 2 cm are melted and formed into a cube. The side of the cube is 6 cm.

Explanation:

We are given two metal rods with dimensions:

1. 5 cm × 8 cm × 3 cm
2. 8 cm × 6 cm × 2 cm

These rods are melted and formed into a cube. We are asked to find the side length of the cube.

Step 1: Calculate the volume of the two rods

The volume of a rectangular prism (rod) is given by the formula:

V = length × width × height

Volume of the first rod:

V₁ = 5 × 8 × 3 = 120 cm³

Volume of the second rod:

V₂ = 8 × 6 × 2 = 96 cm³

Step 2: Find the total volume of the two rods

The total volume of the two rods is:

V_total = V₁ + V₂

= 120 + 96

= 216 cm³

Step 3: Volume of the cube

The volume of the cube is equal to the total volume of the rods.

The volume V of a cube is given by:

V = side³

Let the side length of the cube be s. Therefore:

s³ = 216

Step 4: Solve for the side length

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

`s = root(3)(216) = 6` cm