+4 I have a bale of hay that is 5' in diameter and 4' wide. If I store the bale outside, the outer 8 inches gets damaged by sun and rain. What is the volume of hay that is damaged? Answer in cubic feet and as a percentage of the bale.
+33658 The volume of the full bale is V = w*pi*d2/4 where w is width and d is diameter.
If damage depth is s then the undamaged inner cylinder has volume Vu = (w-2s)*pi*(d-2s)2/4 because the width reduces by s at both left and right, and the diameter reduces by s on "both" sides.
The damaged volume is therefore the difference between these. Here, we have w = 4', d = 5' and s = (2/3)' (because 8" is 2/3 of a foot). So:
V=4×π×524⇒V=78.539816339744831 cubic ft.
Vu=(4−2×23)×π×(5−2×23)24⇒Vu=28.1579785988418505 cubic ft.
Damaged volume Vd ≈ 78.54 - 28.16 = 50.38 cubic ft.
As a percentage Vd/V ≈ 100*50.38/78.54 = 64.15%
+33658 The volume of the full bale is V = w*pi*d2/4 where w is width and d is diameter.
If damage depth is s then the undamaged inner cylinder has volume Vu = (w-2s)*pi*(d-2s)2/4 because the width reduces by s at both left and right, and the diameter reduces by s on "both" sides.
The damaged volume is therefore the difference between these. Here, we have w = 4', d = 5' and s = (2/3)' (because 8" is 2/3 of a foot). So:
V=4×π×524⇒V=78.539816339744831 cubic ft.
Vu=(4−2×23)×π×(5−2×23)24⇒Vu=28.1579785988418505 cubic ft.
Damaged volume Vd ≈ 78.54 - 28.16 = 50.38 cubic ft.
As a percentage Vd/V ≈ 100*50.38/78.54 = 64.15%
