Let the radius of the cone's base be \(r\) 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 radius of the cone's base cannot be negative, the radius of the base is 4.2 cm.