29 Views

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


Team Careers360 5th Jan, 2024
Answer (1)
Team Careers360 18th Jan, 2024

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.

Know More About

Related Questions

TOEFL ® Registrations 2024
Apply
Accepted by more than 11,000 universities in over 150 countries worldwide
Manipal Online M.Com Admissions
Apply
Apply for Online M.Com from Manipal University
View All Application Forms

Download the Careers360 App on your Android phone

Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile

150M+ Students
30,000+ Colleges
500+ Exams
1500+ E-books