A cuboid water tank with dimensions $12$ cm by $12$ cm by $32$ cm contains water to \(\frac{3}

Question

A cuboid water tank with dimensions $12$ cm by $12$ cm by $32$ cm contains water to $\frac{3}{4}$ its height and is used to fill water to a number of identical open cylindrical cans with diameter $4$ cm and height $h$ cm. Assume the thickness of all containers is negligible. Find the volume of water contained in the cuboid tank. Given that the maximum number of cylinder cans that can be completely filled is $8$, find the integer value of $h$. Hence, find the volume of remaining water in the tank. Given that $h = 4$ cm, find the maximum number of cylinder cans that can be completely filled. Hence, find the volume of remaining water in the tank. Part (b) does not specify a unique integer height. The full condition allows $h=31,32,33$ or $34\text{ cm}$; the solution lists the corresponding remainders. A request for the greatest possible integer height would select $34\text{ cm}$.

Accepted Answer

(a) $3456\text{ cm}^3$ (b) As written, $h=31,32,33$, or $34\text{ cm}$, so the remainder is not unique. If the greatest possible integer height is additionally required, $h=34\text{ cm}$ and $37.9\text{ cm}^3$ remains. (c) $68$ cans and $37.9\text{ cm}^3$ remains

Volume and Surface Area of Cylinder

Volume and Surface Area of Cylinder

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