Floating barrel

Barrel (cylinder shape) floats on water, top of barrel is 8 dm above water and the width of surfaced barrel part is 23 dm. Barrel length is 24 dm.

Calculate the volume of the barrel.

Result

V =  11343.3 dm³

Solution:

$d = 24 \ \\ v = 8 \ \\ a = 23 \ \\ r^2 = (a/2)^2 + (r-v)^2 \ \\ r^2 = (a/2)^2 + r^2-2rv+v^2 \ \\ 0 = (a/2)^2 -2rv+v^2 \ \\ 2rv = (a/2)^2 +v^2 \ \\ r = (v^2+(a/2)^2)/(2 \cdot \ v) = (8^2+(23/2)^2)/(2 \cdot \ 8) = \dfrac{ 785 }{ 64 } \doteq 12.2656 \ \\ V = \pi \cdot \ r^{ 2 } \cdot \ d = 3.1416 \cdot \ 12.2656^{ 2 } \cdot \ 24 \doteq 11343.3277 = 11343.3 \ dm^3$

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