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A gear prototype is built to a scale of 1:5. If the prototype has a diameter of 6 cm, what is the actual diameter of the gear?

Mathematics

ScanSolve AI Answer

Answer

30 cm\text{30 cm}

Step-by-step solution

3 steps

  1. Identify the given scale and prototype measurement.

    The scale is 1:51:5. This means that for every 1 unit on the prototype, there are 5 units on the actual gear.
    The prototype diameter is 6 cm6 \text{ cm}.

  2. Set up the ratio to find the actual diameter.

    Let DpD_p be the prototype diameter and DaD_a be the actual diameter.
    The scale can be written as a ratio:

    DpDa=15\frac{D_p}{D_a} = \frac{1}{5}

  3. Substitute the given prototype diameter and solve for the actual diameter.

    6 cmDa=15\frac{6 \text{ cm}}{D_a} = \frac{1}{5}

    To find DaD_a, multiply both sides by 5×Da5 \times D_a:

    Da=5×6 cmD_a = 5 \times 6 \text{ cm} Da=30 cmD_a = 30 \text{ cm}

    The machinists must produce a diameter of 30 cm.

    30 cm\text{30 cm}
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