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Geometry Level 5

Given figure is the 2 D 2D view of cube ( 10 m × 10 m × 10 m ) (10\text{ m}\times10\text{ m}\times10\text{ m}) which has 600 m 3 600\text{ m}^3 of water (dotted part), if cube is tilted with an angle θ \theta such that A B = 2 m AB=2\text{ m} , find the measure of θ \theta in degrees.

Give your answer to 3 decimal places.

this problem is original


The answer is 51.3409.

Atul Shivam by Atul Shivam , 23, India

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1 solution

Let EF=x. The area on the shown side=1/2 * (x + 2)*10. But it is 10 deep. So 600=1/2 * (x + 2) *100. So x=10.
Let EG=AB=2, G along DE. So in right Δ \Delta . FBG, angle GFB=ArcTan(10/8)=51.3402. Since water level BF is horizontal, this is also = θ . \theta. . It may be noted that F coincides with D and the water is ready to flow out !!

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