A conical vessel whose internal radius is 10 cm and height 48 cm is full of water. If this water is poured into a cylindrical vessel with internal radius 20 cm, the height to which water rises in it is:

(Take π = 3.14)

1. 3 cm

2. 4 cm

3. 5 cm

4. 6 cm

Given, radius of cone, R = 10 cm

Height of cone, H = 48 cm

Height of water in cylinder be h cm

Radius of cylinder, r = 20 cm

Since, water from conical vessel is poured into cylindrical vessel.

∴ Volume of cone = Volume of water in cylinder

$\Rightarrow \dfrac{1}{3}π \text{R}^2 \text{H} = π \text{r}^2 \text{h} \\[1em] \Rightarrow \dfrac{1}{3} \times 10^2 \times 48 = 20^2 \times \text{h} \\[1em] \Rightarrow 100 \times 16 = 400 \times \text{h} \\[1em] \Rightarrow \text{h} = \dfrac{100 \times 16}{400} \\[1em] \Rightarrow \text{h} = \dfrac{1600}{400} \\[1em] \Rightarrow \text{h} = 4 \text{ cm.}$

Hence, option 2 is the correct option.