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# 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

### Explanation:

Volume of sphere = Volume of cylinder

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

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

r3 = $$\frac{\pi \times 9 \times 4 \times 3}{4 \pi}$$

r = 3$$\sqrt{27}$$

= 3

## Dicussion (1)

• Volume of sphere = Volume of cylinder

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

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

r3 = $$\frac{\pi \times 9 \times 4 \times 3}{4 \pi}$$

r = 3$$\sqrt{27}$$

= 3