Question

Three cubes of metal whose edges are $6cm,8cmand10cm$ respectively are melted to form a single cube. The edge of the new cube is :

• A. $12$
• B. $24$
• C. $18$
• D. $20$

Answer 1

The correct option is A

$12$

Step 1: Find the volume of the single cube formed by melting three cubes whose edges are $6cm,8cmand10cm$ respectively

A cube is a three-dimensional shape that is defined $XYZ$ plane. It has six faces, eight vertices and twelve edges. All the faces of the cube are in square shape and have equal dimensions.

$\because$ Volume of a cube of edges $\text{a}$ is given by ${\text{a}}^3$

Given that, Three cubes of metal whose edges are $6cm,8cmand10cm$ respectively are melted to form a single cube.
$\therefore$The sum of the volume of the three metal cubes$=6^3+8^3+{10}^3$

$V=216+512+1000$

$V=1728c{m}^3$

Step 2: Find the edge of the new cube

Let the side of the new cube be $“a”$
The volume of the new cube$=$sum of the volume of three cubes

$a^3=1728$

$$\begin{gathered} a^3={12}^3 \\ a=12cm \end{gathered}$$
Hence the correct option is option A.