Question

66 cubic centimetres of silver is drawn into a wire of 1mm diameter. The length of the wire in metres will be :

• A. 84
• B. 90
• C. 168
• D. 336

Answer 1

The Correct Option is A

To determine the length of the wire in metres when 66 cubic centimetres of silver is drawn into a wire of 1mm diameter, we start by recognizing the shape and properties of the wire. The wire has a cylindrical shape, and we're given two key parameters: the volume (\(V\)) of the silver and the diameter (\(d\)) of the wire. 

The volume \(V\) of a cylinder is calculated using the formula:

\(V = \pi r^2 h\)

where:

• \(V = 66 \, \text{cm}^3\) (given)
• \(r\) is the radius of the wire, which is half of the diameter
• \(h\) is the height (or in this case, the length) of the wire

The diameter of the wire is 1mm, which is \(0.1 \, \text{cm}\) (since \(1 \, \text{mm} = 0.1 \, \text{cm}\)). Thus, the radius \(r\) is half of this diameter:

\(r = \frac{0.1}{2} = 0.05 \, \text{cm}\)

Substituting the known values into the volume formula, we have:

\(66 = \pi (0.05)^2 h\)

Solving for \(h\), the length of the wire, we get:

\(66 = \pi \times 0.0025 \times h\)

\(66 = 0.00785h\)

\(h = \frac{66}{0.00785}\)

Calculating the above, we find:

\(h \approx 8403.82 \, \text{cm}\)

Since we need the length in metres, we convert centimetres to metres by dividing by 100:

\(h \approx \frac{8403.82}{100} = 84.0382 \, \text{m}\)

Rounding this, the length of the wire is approximately 84 metres, which matches the correct answer option.

Answer: 84 metres