A cylindrical can of internal radius 7 cm holds water to a depth of 12 cm. All of this water is tipped into an empty conical vessel of internal radius 14 cm standing point downwards, and it fills the cone exactly to the brim. How deep is the cone, in cm?

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Accepted Answer

9. Water carried across = πr²h = π × 49 × 12 = 588π cm³. In the cone, (1/3)π × 14² × h = (196/3)πh, so (196/3)h = 588 and h = (588 × 3)/196 = 9 cm. (Treating the cone as a cylinder — no 1/3 — gives 3 cm; using the can's radius 7 cm for the cone as well gives 36 cm; 12 cm assumes the depth is unchanged, but the cone is wider and slants, so it cannot be.)

A cylindrical can of internal radius 7 cm holds water to a depth of 12 cm. All of this water is tipped into an empty conical vessel of internal radius 14 cm standing point downwards, and it fills the cone exactly to the brim. How deep is the cone, in cm?

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