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# General Maths Problem 01

solve this problem

Note by Ajitesh Mishra
3 years, 5 months ago

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Let $$X$$ and $$Y$$ be the heights of the big and small cylinder respectively. In figure B height of water in the small cylinder is inadvertently $$X-20$$. So, the Volume occupied by water $$=\pi3^2X+\pi 1^2(20-X)$$ $$\Rightarrow V=20\pi+8\pi X$$ In figure $$C$$ height of water in small cylinder is simply $$Y$$ and that in the bigger one is$$28-Y$$ In figure $$C$$, $$V=\pi Y +9\pi (28-Y)$$ $$\Rightarrow V=252\pi-8\pi Y$$ Equating the two volume equations, gives us: $$20\pi+8\pi X=252\pi-8\pi Y$$ $$\Rightarrow X+Y=29 cm$$ which is the height of the bottle. · 3 years, 5 months ago