**A sphere of radius rcm has the same volume as cylinder of radius 3cm and height ...**

### Question

A sphere of radius rcm has the same volume as cylinder of radius 3cm and height 4cm. Find the value of r### Options

A) \(\frac{2}{3}\)

B) 2

C) 3

D) 6

The correct answer is C.

### Explanation:

Volume of sphere = Volume of cylinder

i.e. \(\frac{4}{3} \pi r^3 = \pi r^2 h\)

\(\frac{4}{3} \pi r^3 = \pi \times 3^2 \times 4\)

r^{3} = \(\frac{\pi \times 9 \times 4 \times 3}{4 \pi}\)

r = 3\(\sqrt{27}\)

= 3

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Volume of sphere = Volume of cylinder

i.e. \(\frac{4}{3} \pi r^3 = \pi r^2 h\)

\(\frac{4}{3} \pi r^3 = \pi \times 3^2 \times 4\)

r

^{3}= \(\frac{\pi \times 9 \times 4 \times 3}{4 \pi}\)r = 3\(\sqrt{27}\)

= 3