Question:
Three solid cubes of sides 1 cm, 6 cm and 8 cm are melted to form a new cube. Find the surface area of the cube so formed.
Three solid cubes of sides 1 cm, 6 cm and 8 cm are melted to form a new cube. Find the surface area of the cube so formed.
Updated On: Dec 21, 2025
- 729 cm2
- 486 cm2
- 125 cm2
- 529 cm2
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The Correct Option is B
Solution and Explanation
To find the surface area of the new cube formed by melting three solid cubes with sides measuring 1 cm, 6 cm, and 8 cm, we will follow these steps:
Calculate the volume of each cube:
- The volume of the first cube with side 1 cm is: \(1^3 = 1 \, \text{cm}^3\)
- The volume of the second cube with side 6 cm is: \(6^3 = 216 \, \text{cm}^3\)
- The volume of the third cube with side 8 cm is: \(8^3 = 512 \, \text{cm}^3\)
Find the total volume of the new cube, which is the sum of the volumes of the individual cubes:
\(1 + 216 + 512 = 729 \, \text{cm}^3\)
Determine the side length of the new cube using the formula for the volume of a cube: \(V = a^3\), where \(a\) is the side length.
Set the equation: \(a^3 = 729\)
By taking the cube root of both sides, we find: \(a = \sqrt[3]{729} = 9 \, \text{cm}\)
Calculate the surface area of the cube with side 9 cm using the surface area formula of a cube: \(6a^2\).
\(6 \times 9^2 = 6 \times 81 = 486 \, \text{cm}^2\)
Therefore, the surface area of the cube formed by melting the given cubes is 486 cm2.
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