A metallic sphere of volume 3136π cm³ is melted and then, recast into smaller cones, each of radius 3.5 cm and height 4 cm. How many cones are obtained?

Correct option is B

Given Data:
· Volume of sphere = 3136π  $$cm^3$$​​
· Radius of cone = 3.5 "cm"
· Height of cone = 4 "cm"
Formulas Used:
Volume of a sphere:
​$$V=\frac{4}{3}πr^3$$​​
Volume of a cone:
​$$V=\frac{1}{3} πr^2 h$$​​
Solution:
Volume of the cone:

​$$V=\frac{1}{3}π(3.5)^2 (4)=\frac{1}{3}π(12.25)(4)=\frac{49}{3}π cm^3$$​​
Calculate the number of cones:
Number of cones = $$\frac{Volume \ of \ sphere }{Volume \ of \ cone } =\frac{3136π}{(\frac{49}{3} π)}=\frac{(3136×3)}{49}=192$$​​
Answer: (b) 192