Assertion (A) : Two solid spheres of radii 2 cm and 4 cm are melted and recast into a cone of radius 6 cm. The height of the cone so obtained will be 8 cm.

Reason (R) : When we convert one solid into another, the volume of the two solids remains the same.

1. A is true, R is the false

2. A is false, R is true

3. Both A and R are true

4. Both A and R are false

Given,

Radius of first solid sphere, r = 2 cm

Radius of second solid sphere, R = 4 cm

Height of cone be h cm

Radius of cone, a = 6 cm

Since, two spheres are melted and recasted into cone.

∴ Volume of 1st sphere + Volume of 2nd sphere = Volume of cone

$\therefore \dfrac{4}{3} π\text{r}^3 + \dfrac{4}{3} π\text{R}^3 = \dfrac{1}{3} π\text{a}^2\text{h} \\[1em] \Rightarrow \dfrac{4}{3} π(\text{r}^3 + \text{R}^3) = \dfrac{1}{3} π\text{a}^2\text{h} \\[1em] \Rightarrow 4(\text{r}^3 + \text{R}^3) = \text{a}^2\text{h} \\[1em] \Rightarrow 4(2^3 + 4^3) = 6^2\text{h} \\[1em] \Rightarrow 4(8 + 64) = 36\text{h} \\[1em] \Rightarrow 4(72) = 36\text{h} \\[1em] \Rightarrow \text{h} = \dfrac{288}{36} \\[1em] \Rightarrow \text{h} = 8 \text{ cm.}$

∴ Assertion (A) is true.

Since, one solid is melted and converted into another, the volume of the two solids remains the same.

∴ Reason (R) is true.

Hence, option 3 is the correct option.