Let radius of cylinder = r. Diameter of cylinder = 2r
Height of cylinder = [tex] \frac{2}{3} (2r)= \frac{4r}{3} [/tex] .....[Given]
Volume of cylinder = [tex] \pi x^{2} h= \pi x^{2} ( \frac{4r}{3} )= \frac{4 x^{3} }{3} [/tex]
Volume of sphere with radius 4 cm =[tex] \frac{4}{3} \pi (4) ^{3} = \frac{4}{3} \pi (64)[/tex]
According to the question,
Volume of cylinder = Volume of sphere
=>[tex] \frac{4}{3} \pi x^{3} = \frac{4}{3} \pi (4) ^{3} =\ \textgreater \ r^{3} =(4)^{3} =\ \textgreater \ r = 4cm[/tex]
Hence, radius of base of cylinder = 4cm
