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A shallow shaft has a cross-sectional area of 125.6 cm² and a bore of 8 cm diameter. Calculate the outer diameter of the shaft. Give your answer to 2 significant figures.

a) 6.77 cm
b) 10.64 cm
c) 12.66 cm
d) 14.13 cm

1 Answer

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Final answer:

The outer diameter of the shaft is approximately 5.6 cm.

Step-by-step explanation:

To calculate the outer diameter of the shaft, we need to first find the radius of the bore. The bore has a diameter of 8 cm, so the radius is half of that, which is 4 cm. The cross-sectional area of the shaft is given as 125.6 cm². Since the cross-sectional area of a circle is equal to πr², where r is the radius, we can set up the equation 125.6 cm² = π(4 cm)².

Simplifying the equation, we have 125.6 cm² = 16π cm². To find the value of π, we can use an approximate value of 3.14. Thus, 125.6 cm² = 16(3.14) cm². Dividing both sides of the equation by 16, we get 7.85 cm² = 3.14 cm².

To find the radius of the outer diameter, we can take the square root of the cross-sectional area: √(7.85 cm²) ≈ 2.8 cm. The outer diameter is then twice the radius, so the answer is 2(2.8 cm) = 5.6 cm. Rounded to 2 significant figures, the outer diameter of the shaft is approximately 5.6 cm.

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