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Calculate the shape descriptors: Sphericity, Aspect Ratio, Elongation Ratio, and Flatness Ratio given Length (7.0 mm), Width (2.5 mm), and Thickness (2.0 mm).

Mathematics

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4 parts
a(i)
0.467
a(ii)
0.357
a(iii)
2.8
a(iv)
0.8

Step-by-step solution

12 steps

Here is the solution to the exam question:

Part a(i)· 3 steps

Sphericity (SS)

Calculate the shape descriptors

Given dimensions:

  • Length (LL) = 7.0 mm7.0 \text{ mm}
  • Width (WW) = 2.5 mm2.5 \text{ mm}
  • Thickness (TT) = 2.0 mm2.0 \text{ mm}

  1. State the formula for Sphericity.

    S=(LWT)1/3LS = \frac{(LWT)^{1/3}}{L}

  2. Substitute the given values into the formula.

    S=(7.0 mm×2.5 mm×2.0 mm)1/37.0 mmS = \frac{(7.0 \text{ mm} \times 2.5 \text{ mm} \times 2.0 \text{ mm})^{1/3}}{7.0 \text{ mm}} S=(35.0 mm3)1/37.0 mmS = \frac{(35.0 \text{ mm}^3)^{1/3}}{7.0 \text{ mm}} S=3.271 mm7.0 mmS = \frac{3.271 \text{ mm}}{7.0 \text{ mm}}

  3. Calculate the Sphericity.

    S≈0.467S \approx 0.467

    The sphericity is:

    0.467\boxed{0.467}

Part a(ii)0.357

Aspect Ratio (RaR_a)

  1. State the formula for Aspect Ratio.

    Ra=WLR_a = \frac{W}{L}

  2. Substitute the given values into the formula.

    Ra=2.5 mm7.0 mmR_a = \frac{2.5 \text{ mm}}{7.0 \text{ mm}}

  3. Calculate the Aspect Ratio.

    Ra≈0.357R_a \approx 0.357

    The aspect ratio is:

    0.357\boxed{0.357}

Part a(iii)2.8

Elongation Ratio (ReR_e)

  1. State the formula for Elongation Ratio.

    Re=LWR_e = \frac{L}{W}

  2. Substitute the given values into the formula.

    Re=7.0 mm2.5 mmR_e = \frac{7.0 \text{ mm}}{2.5 \text{ mm}}

  3. Calculate the Elongation Ratio.

    Re=2.8R_e = 2.8

    The elongation ratio is:

    2.8\boxed{2.8}

Part a(iv)0.8

Flatness Ratio (RfR_f)

  1. State the formula for Flatness Ratio.

    Rf=TWR_f = \frac{T}{W}

  2. Substitute the given values into the formula.

    Rf=2.0 mm2.5 mmR_f = \frac{2.0 \text{ mm}}{2.5 \text{ mm}}

  3. Calculate the Flatness Ratio.

    Rf=0.8R_f = 0.8

    The flatness ratio is:

    0.8\boxed{0.8}

Part b

Briefly explain what the calculated Elongation Ratio (ReR_e) tells you about the shape of this rice grain.

The calculated Elongation Ratio (Re=2.8R_e = 2.8) indicates that the rice grain is significantly elongated. Specifically, its length is 2.8 times greater than its width, confirming it has a long, slender shape rather than being round or flat.

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