The curved surface area of a cone is $550{\text{cm}}^2$ and its base radius is 7 cm. Find its vertical height in cm. Take π = 22/7.

From π$rl=550,(22/7)(7)l=22l=550$, so the slant height $l=25$ cm. The vertical height then comes from $l^2=r^2+h^2:h$ = √(625 − 49) = √576 = 24 cm. (25 cm is the slant height, one step short; subtracting the lengths rather than their squares, 25 − 7, gives 18 cm; using 2π$rl$ for the curved surface halves the slant height to 12.5 cm and gives √(156.25 − 49) ≈ 10.36 cm.)