A hollow shaft has a cross sectional area of 8.68 cm^2.If its inside diameter is 0.75cm, calculate its outside diameter.
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To calculate the outside diameter of a hollow shaft, we need to know its inside diameter and the cross-sectional area.
The cross-sectional area of a hollow shaft can be calculated using the formula:
A = π * (R2 - r2),
where A is the cross-sectional area, R is the outside radius, and r is the inside radius.
In this case, we know that the cross-sectional area is 8.68 cm^2 and the inside diameter is 0.75 cm.
First, we need to convert the inside diameter to the inside radius by dividing it by 2:
r = 0.75 cm / 2 = 0.375 cm.
Now, we can rearrange the formula to solve for the outside radius:
R2 = A / π + r2.
Substituting the given values:
R2 = 8.68 cm^2 / π + (0.375 cm)^2.
R2 = 8.68 cm^2 / 3.1416 + 0.140625 cm^2.
R2 = 8.68 cm^2 / 3.1416 + 0.140625 cm^2.
R2 ≈ 2.76 cm^2 + 0.140625 cm^2.
R2 ≈ 2.900625 cm^2.
Now, we can find the square root of R^2 to get R:
R ≈ √(2.900625 cm^2).
R ≈ 1.7 cm (approx).
Finally, to find the outside diameter, we multiply the outside radius by 2:
Outside Diameter = 2 * R ≈ 2 * 1.7 cm.
Therefore, the outside diameter of the hollow shaft is approximately 3.4 cm.