Question : A cylindrical metallic rod of diameter 2 cm and length 45 cm is melted and converted into wire of uniform thickness and length 5 m. The diameter of the wire is:
Option 1: 3 mm
Option 2: 2 mm
Option 3: 6 mm
Option 4: 5 mm
Correct Answer: 6 mm
Solution :
Given,
A cylindrical metallic rod of diameter 2 cm and length 45 cm is melted and converted into wire of uniform thickness and length 5 m.
Let $V_1$ and $V_2$ be the volumes of the cylindrical rods in the two cases.
According to the question,
$V_1=V_2$
We know the volume of cylinder = $\pi r^2h$, where r is the radius and h is the height
⇒ $\pi r_1^2h_1=\pi r_2^2h_2$
⇒ $ r_1^2h_1=r_2^2h_2$
⇒ $(10)^2\times 450=r_2^2\times 5000$ [As 5 m = 5000 mm and 1 cm = 10 mm]
⇒ $r_2^2=\frac{450\times 10\times 10}{5000}$
⇒ $r_2^2=9$
⇒ $r_2=3$ mm
⇒ diameter = 3 × 2 = 6 mm
Hence, the correct answer is 6 mm.
Related Questions
Know More about
Staff Selection Commission Sub Inspector ...
Result | Eligibility | Application | Selection Process | Cutoff | Admit Card | Preparation Tips
Get Updates Brochure
Your Staff Selection Commission Sub Inspector Exam brochure has been successfully mailed to your registered email id “”.
