A circular pipe has an external diameter of 100 mm and internal diameter of 80 mm. What is the cross-sectional area of the metal?
- 1570.8 sq mm, because area = pi x (D-d)/2 = pi x 10 = 31.4 but x 50 = 1570.8, using perimeter method not area formula
- 7854 sq mm, because area = pi/4 x D^2 = pi/4 x 10000 = 7854 sq mm as the circular area that the outer diameter defines
- 2827.4 sq mm, because area = pi/4(D^2-d^2) = pi/4(10000-6400) = pi/4 x 3600 = 2827.4 sq mm for the ring section area
Explanation from PART66Online
The metal cross-section is the outer circle's area minus the bore, so area = (pi/4)(D^2 - d^2). With D = 100 and d = 80, this is (pi/4)(10000 - 6400) = (pi/4) x 3600 = 2827.4 sq mm. Using only the external diameter (7854) ignores the hollow centre.
K
kpaximadakes asked · 1h ago
Why pi/4 and not just pi. It is about the area right?
Community Comments (1)
P
PART66Online
1h ago
Yes, it is the area. The area of a circle is A = pi x r^2, but in this question you are given diameters, not radii. Since r = D/2:
A = pi x (D/2)^2 = pi x D^2/4
So pi/4 is not an extra factor. It is just what pi x r^2 becomes when you write it with the diameter instead of the radius.
The metal is the ring between the two circles, so you take the outer area minus the inner area:
A = pi/4 x (100^2 - 80^2) = pi/4 x 3600 = 2827.4 sq mm
With radii you get the same result: pi x (50^2 - 40^2) = pi x 900 = 2827.4 sq mm.
If you used just pi with the diameters, you would get pi x 3600 = 11,310 sq mm, which is four times too big.
A = pi x (D/2)^2 = pi x D^2/4
So pi/4 is not an extra factor. It is just what pi x r^2 becomes when you write it with the diameter instead of the radius.
The metal is the ring between the two circles, so you take the outer area minus the inner area:
A = pi/4 x (100^2 - 80^2) = pi/4 x 3600 = 2827.4 sq mm
With radii you get the same result: pi x (50^2 - 40^2) = pi x 900 = 2827.4 sq mm.
If you used just pi with the diameters, you would get pi x 3600 = 11,310 sq mm, which is four times too big.
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