Expert: Ahmed Salami - 4/30/2009

Question
the volume v of a conical solid, radius r th subject of the formula. V=1/3 pie r squared h, transpose formula to make r the subject. and then calculate the radius of the conical when the the volume is 17000cm cubed and h=40cm.need to know how to do this in case this sort of question comes up in a maths exam

Answer
Hi Helen,
The formula V = (1/3)#r^2.h (where # represents pi) gives the value of the volume given the values of the radius and height of the conical solid. Suppose we had the value of the volume already and the value of the height so that we now need the value of the radius, we have to work backwards but this can be made straightforward when we've transposed the formula so that the radius is easily gotten from the values of V and h. We do this in the following way;
V = (1/3)#r^2.h
 = [(1/3).#.h.]r^2
dividing both sides by the coefficient of r^2
V = [(1/3).#.h.]r^2
V/[(1/3).#.h.] = r^2
3V/#h = r^2
taking the square root of both sides,
sqrt(3V/#h) = r
and so the formula for r is
r = sqrt(3V/#h)
when V = 17000cm^3 and h = 40cm
r = sqrt(3x17000/#x40)
 = sqrt(51000/125.66)
 = sqrt 405.85
 = 20.15cm

Hope it helps you.

Regards