If the radius of a sphere is increased by 2 cm, then its surface area increases by 704 $$cm^2$$. Using $$\pi = \frac{22}{7}$$, find the radius of the sphere after the increase.​

Correct option is B

Given:

Radius of a sphere is increased by 2 cm,

Surface area increases by 704 $$cm^2$$​ 

Formula Used:

Surface area of sphere = $$4\pi r^2$$​

Solution:

New surface area = $$4\pi(r+2)^2$$​

Increase in surface area is given as 704 cm²

​$$4\pi(r + 2)^2- 4\pi r^2 = 704$$​​

​$$4\pi[(r+2)^2 - r^2]= 704$$

$$4\pi[(r^2 +4+4r)-r^2] = 704\\ 4\pi[r^2 +4+4r-r^2] = 704\\4\pi[4+4r] = 704\\$$

Take 4 common from the brackets
$$16\pi[(1+r)]= 704$$

1 + r = $$\frac{704\times7}{16\times22}$$

1 + r = 14

r = 14 -1 = 13

After increase, Radius will be 13+ 2 = 15 cm