If three metallic spheres of radii 3 cm. 4 cm and 5 cm respectively are melted to form a single sphere then what will be the volume of the new sphere?$$\left(\pi=\frac{22}7\right)$$​

Correct option is A

Given: 

Radii of smaller spheres = 3 ,4, 5 cm respectively  

Formula Used:

Volume of Sphere = $$\frac43\pi{r}^3$$​​

Solution: 

Volume of bigger Sphere = Sphere a  volume + Sphere b volume + Sphere a volume,

= $$\frac43\pi{3}^3$$ + $$\frac43\pi{4}^3$$ + $$\frac43\pi{5}^3$$ 

= $$\frac43\pi27+\frac43\pi64+\frac43\pi125$$

= $$\frac 4 3 \pi \left(27 + 64+125 \right)$$ ​

= $$\frac{108\pi}3+\frac{256\pi}3+\frac{500\pi}3$$

= $$\frac{864\pi}3 = \frac{288\times22}7$$​​

=$$\frac{6336}7$$ 

= $$905\frac17 \ cm^3$$

Thus, the volume of the bigger sphere is $$905\frac17 \ cm^3$$​​