A cylinder drum with an open top and height of 90 cm is filled to the top with 210 L of water. What is the remaining volume of water (in L ) when the drum is tilted 1 0 ∘ with the vertical? (Give your answer to the nearest integer.)
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Typo in the figure. t a n ( 1 0 ) 2 r
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No, it is correct. 2 r h = tan 1 0 ∘ ⟹ h = 2 r tan 1 0 ∘ . I used this fact in the calculations.
Sorry. I made the mistake because your h and my h are different.
H e i g h t o f w a t e r a t t h e o t h e r e n d h 1 = 9 0 − 2 r ∗ T a n ( 1 0 ) c m .
r
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3
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1
8
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9
9
L
V=pi (R^2)[H-2R Tan(x)+R Tan(x)], H=90 R=sqrt[0.21 10^6/(H*pi)]=27.253, x=10 degree V=198.78, Answer=199
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We note that the volume of water spilled out Δ V is a half of the volume of a cylinder same radius r as the drum but with a height of 2 r tan 1 0 ∘ . In equation,
Δ V = 2 h 2 r tan 1 0 ∘ V = tan 1 0 ∘ π h 3 1 0 0 0 V 3 = tan 1 0 ∘ π ⋅ 9 0 3 1 0 0 0 ⋅ 2 1 0 3 ≈ 1 1 . 2 where h and V are the height and volume of the drum. Note that r = π h 1 0 0 0 V and V = 2 1 0 and h = 9 0
Therefore the remaining volume of water V − Δ V = 2 1 0 − 1 1 . 2 ≈ 1 9 9 L .