The number of solid spheres, each of diameter 6 cm that can be moulded to form a solid metal cylinder of height 45 cm and diameter 4 cm, is :

1. 3

2. 4

3. 5

4. 6

Given,

Diameter of sphere = 6 cm

Radius of sphere, r = $\dfrac{\text{diameter}}{2} = \dfrac{6}{2}$ = 3 cm

Height of cylinder, h = 45 cm

Diameter of cylinder = 4 cm

Radius of cylinder, R = $\dfrac{\text{diameter}}{2} = \dfrac{4}{2}$ = 2 cm

Number of solid spheres required be n.

Since, the number of solid spheres, are moulded to form a solid metal cylinder.

∴ Volume of cylinder = n × Volume of solid sphere

$\Rightarrow π\text{R}^2\text{h} = \text{n} \times \dfrac{4}{3}π \times \text{r}^3 \\[1em] \Rightarrow \text{R}^2\text{h} = \text{n} \times \dfrac{4}{3} \times \text{r}^3 \\[1em] \Rightarrow 2^2 \times 45 = \text{n} \times \dfrac{4}{3} \times 3^3 \\[1em] \Rightarrow 4 \times 45 = \text{n} \times \dfrac{4}{3} \times 27 \\[1em] \Rightarrow 180 = \text{n} \times 4 \times 9 \\[1em] \Rightarrow 180 = \text{n} \times 36 \\[1em] \Rightarrow \text{n} = \dfrac{180}{36} \\[1em] \Rightarrow \text{n} = 5.$

Hence, option 3 is the correct option.