When a right triangle of area $4$ is rotated $360^o$ about its longer leg, the solid that results has a volume of $16$. Calculate the volume of the solid that results when the same right triangle is rotated about its shorter leg.

Let the legs be a and b. Area = 0.5*a*b = 4, so ab = 8. Rotating about 'a' gives a cone with radius b and height a: Volume = (1/3)pi*b^2*a = 16. Thus, (1/3)*pi*b(ab) = 16 => (1/3)pi*b*8 = 16 => b = 6/pi. Then a = 8/b = 8/(6/pi) = 4*pi/3. Rotating about 'b' gives volume = (1/3)*pi*a^2*b = (1/3)*pi*a(ab) = (1/3)pi(4*pi/3)*8 = 32*pi^2/9 approx 35.09.