Question

The internal \(d_i\) and external \(d_o\) diameters of a Shelby sampler are 48 mm and 52 mm, respectively. The area ratio (\(A_r\)) of the sampler (in %, round off to two decimal places) is _______________

Answer 1

Correct Answer: 17.25 - 17.45

The area ratio \(A_r\) of the Shelby sampler is calculated using the formula:

\[ A_r = \left( \frac{d_o^2 - d_i^2}{d_i^2} \right) \times 100 \]

Given \(d_i = 48 \, \text{mm}\) and \(d_o = 52 \, \text{mm}\), we substitute these values into the formula:

\[ A_r = \left( \frac{52^2 - 48^2}{48^2} \right) \times 100 \]

First, calculate the squares:

\[ 52^2 = 2704, \quad 48^2 = 2304 \]

Then, find the difference:

\[ 2704 - 2304 = 400 \]

Now, divide by \(48^2\):

\[ \frac{400}{2304} \approx 0.1736 \]

Multiply by 100 to get the percentage:

\[ 0.1736 \times 100 = 17.36\% \]