a hollow shaft has a cross sectional area of 8.68 cm square if its inside diameter is 0.75 cm, calculate its outside diameter.
pi (Rout^2 - Rin^2) = 8.68
In other words just hollow out the shaft.
Why did the hollow shaft go to therapy? It had an identity crisis! Nevertheless, let's solve your problem.
We know that the cross-sectional area of the hollow shaft is 8.68 cm² and its inside diameter is 0.75 cm. To find the outside diameter, we need to calculate the difference between the areas of the outer and inner circles.
Area of outer circle = πr² ✔️
Area of inner circle = π(0.375)² ✔️
Now, let's solve this mathematically:
8.68 cm² = πr² - π(0.375)²
Simplifying:
8.68 cm² + π(0.375)² = πr²
Using π ≈ 3.14:
8.68 cm² + 3.14(0.375)² = 3.14r²
Simplifying further:
8.68 cm² + 0.35 cm² ≈ 3.14r²
Combining the areas:
9.03 cm² ≈ 3.14r²
Now, let's solve for r:
9.03 cm² ÷ 3.14 ≈ r²
2.877 cᵐ² ≈ r²
Taking the square root:
√2.877 cᵐ² ≈ r
r ≈ 1.70 cᵐ
Finally, let's find the outside diameter:
Outside diameter = Inside diameter + 2r
Outside diameter ≈ 0.75 cm + 2(1.70 cm)
Outside diameter ≈ 0.75 cm + 3.40 cm
Outside diameter ≈ 4.15 cm
Therefore, the approximate outside diameter of the hollow shaft is 4.15 cm. Keep in mind that this calculation assumes a perfect circular shape and uses approximations.
To calculate the outside diameter of the hollow shaft, we need to use the formula for the area of a circular cross section:
A = π * r^2
Given that the inside diameter of the shaft is 0.75 cm, we can determine the inside radius (r1) by dividing it by 2:
r1 = 0.75 cm / 2 = 0.375 cm
The cross-sectional area (A1) of the shaft can be calculated using the inside radius:
A1 = π * (0.375 cm)^2
Now, we can use the formula for the area of a circular cross section again, but this time using the outside diameter (D2) and the outside radius (r2):
A2 = π * r2^2
To find r2, we can rearrange the formula for A2:
r2 = sqrt(A2 / π)
Given the cross-sectional area (A2) of 8.68 cm^2, we can substitute it into the formula:
r2 = sqrt(8.68 cm^2 / π)
Calculating r2:
r2 = sqrt(2.77 cm^2) ≈ 1.664 cm
Finally, we can find the outside diameter (D2) from the outside radius:
D2 = 2 * r2 = 2 * 1.664 cm ≈ 3.328 cm
Therefore, the outside diameter of the hollow shaft is approximately 3.328 cm.
To calculate the outside diameter of the hollow shaft, we need to know the inside diameter and the cross-sectional area.
The formula to calculate the area of a circular cross-section is:
A = πr^2
Where A is the cross-sectional area and r is the radius.
Given that the cross-sectional area is 8.68 cm^2, we can solve for the radius of the inside diameter:
A = π(0.75/2)^2
8.68 = 3.14(0.375)^2
8.68 = 3.14(0.140625)
8.68 = 0.44109375
We can now rearrange the formula for the area to solve for the radius:
r = √(A/π)
r = √(8.68/3.14)
r = √2.76751592
r ≈ 1.663 cm
The radius of the inside diameter is approximately 1.663 cm.
To calculate the outside diameter, we can double the radius of the inside diameter:
Outside Diameter = 2 × Radius
Outside Diameter ≈ 2 × 1.663 cm
Outside Diameter ≈ 3.326 cm
Therefore, the outside diameter of the hollow shaft is approximately 3.326 cm.