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 \: r {}^{2} h = \pi \: r {}^{2} ( \frac{4\pi}{3} ) = \frac{4\pi \: r {}^{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 \: r {}^{3} = \frac{4}{3} \pi(4) {}^{3} [/tex]
=> [tex]r {}^{3} = (4) {}^{3} [/tex]
=> r = 4
Hence,radius of base of cylinder = 4 cm
