Question

Three cubes of sides 6 cm, 8 cm and 1 cm are melted to form a new cube then the length of the edge of the new cube is

• A. 9 cm
• B. 8 cm
• C. 7 cm
• D. 6 cm

Answer 1

The Correct Option is A

To solve the problem, we need to determine the length of the edge of a new cube formed by melting three cubes with side lengths \(6 \, \text{cm}\), \(8 \, \text{cm}\), and \(1 \, \text{cm}\). The volume of the new cube will be equal to the sum of the volumes of the three original cubes.

Step 1: Calculate the volume of each original cube.
The volume \(V\) of a cube with side length \(a\) is given by:

\[ V = a^3 \]

For the first cube (\(a = 6 \, \text{cm}\)):

\[ V_1 = 6^3 = 216 \, \text{cm}^3 \]

For the second cube (\(a = 8 \, \text{cm}\)):

\[ V_2 = 8^3 = 512 \, \text{cm}^3 \]

For the third cube (\(a = 1 \, \text{cm}\)):

\[ V_3 = 1^3 = 1 \, \text{cm}^3 \]

Step 2: Find the total volume of the three cubes.
The total volume \(V_{\text{total}}\) is the sum of the volumes of the three cubes:

\[ V_{\text{total}} = V_1 + V_2 + V_3 = 216 + 512 + 1 = 729 \, \text{cm}^3 \]

Step 3: Determine the side length of the new cube.
Let the side length of the new cube be \(a_{\text{new}}\). The volume of the new cube is also given by \(a_{\text{new}}^3\). Since the volume of the new cube is equal to the total volume of the three original cubes:

\[ a_{\text{new}}^3 = 729 \]

Solve for \(a_{\text{new}}\) by taking the cube root of both sides:

\[ a_{\text{new}} = \sqrt[3]{729} = 9 \, \text{cm} \]

Final Answer:
The length of the edge of the new cube is \(9 \, \text{cm}\).

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