Assume that the base radius of the cone is \(r\) cm.
\(\therefore \pi r(r + 7) = 147.84\)
or, \(\cfrac{22}{7} r(r + 7) = 147.84\)
or, \( r(r + 7) = \cfrac{\cancel{14784}\cancel{672}168}{\cancel{100}25} \times \cfrac{7}{\cancel{22}}\)
or, \( r^2 + 7r = \cfrac{168 \times 7}{25}\)
or, \(25r^2 + 175r = 1176\)
or, \(25r^2 + 175r - 1176 = 0\)
or, \(25r^2 + 280r - 105r - 1176 = 0\)
or, \(5r(5r + 56) - 21(5r + 56) = 0\)
or, \((5r + 56)(5r - 21) = 0\)
\(\therefore\) Either \(5r + 56 = 0\) or \(r = -\cfrac{56}{5}\)
Or, \(5r - 21 = 0\) or \(r = \cfrac{21}{5} = 4.2\)
Since the base radius of the cone cannot be negative, the base radius of the cone is 4.2 cm.