Question

A copper rod of diameter \(1\) cm and length \(8\) cm is drawn into a wire of length \(18\) meters of uniform thickness. Then the thickness of that wire (in cm) is

• A. \(\frac{1}{30}\)
• B. \(\frac{1}{15}\)
• C. \(\frac{1}{12}\)
• D. \(\frac{1}{9}\)

Hint:

In reshaping solids, volume always remains constant unless material is added or removed.

Answer 1

The Correct Option is B

Concept: When a rod is drawn into a wire, the volume remains the same.

Step 1: Find volume of the rod.
Rod is cylindrical. Diameter: \[ 1 \text{ cm} \] Radius: \[ \frac12 \text{ cm} \] Length: \[ 8 \text{ cm} \] Volume: \[ V=\pi r^2 h \] \[ =\pi\left(\frac12\right)^2(8) \] \[ =\pi \cdot \frac14 \cdot 8 \] \[ =2\pi \]

Step 2: Find volume of wire.
Wire length: \[ 18 \text{ m}=1800 \text{ cm} \] Let radius of wire be: \[ r \] Volume: \[ \pi r^2(1800) \] Since volume is same: \[ \pi r^2(1800)=2\pi \]

Step 3: Solve for radius.
\[ 1800r^2=2 \] \[ r^2=\frac{1}{900} \] \[ r=\frac{1}{30} \] Thickness means diameter: \[ 2r=2\times \frac{1}{30} \] \[ =\frac{1}{15} \] Thus, the thickness of the wire is: \[ \boxed{\frac{1}{15}\text{ cm}} \]