A metal cube of edge 12 cm is melted and formed into three smaller cubes. If the edges of two smaller cubes… · ABC26GN5088
Subject: General Aptitude · Chapter: Volume and Surface Area
A metal cube of edge 12 cm is melted and formed into three smaller cubes. If the edges of two smaller cubes are 6cm and 8cm, find the edges of the third smaller cube. [DMRC-Jr. Engineer (Electrical) Exam 2016]
(a)8 cm
(b)10 cm
(c)12 cm
(d)None of these
Answer
Answer (as printed): B
Explanation
Let Edge of third small cube be $x \mathrm{cm}$ Volume of cube $=(\text { edge })^{3}$ According to the question, $6^{3}+8^{3}+x^{3}=12^{3}$ $$\begin{aligned} & \Rightarrow 216+512+x^{3}=1728 \\ & x^{3}=1728-728=1000 \\ & \Rightarrow x=\sqrt[3]{1000}=10 \mathrm{cm} \end{aligned}$$