If the radius of a sphere is increased by 2cm, its surface area increases by 704cm
2
. What was the radius of the sphere before the increase? (Use π=
7
22
​
)

Let the initial radius of the sphere be rcm.
The formula for the surface area of a sphere is A=4πr
2
.

When the radius is increased by 2cm, the new radius becomes (r+2)cm.
The new surface area is 4π(r+2)
2
.

Given that the surface area increases by 704cm
2
:

4π(r+2)
2
−4πr
2
=704
4π[(r+2)
2
−r
2
]=704
4×
7
22
​
×(r
2
+4r+4−r
2
)=704
7
88
​
×(4r+4)=704
4r+4=
88
704×7
​

Since 88×8=704:

4r+4=8×7
4r+4=56
4r=52
r=13cm
Therefore, the initial radius of the sphere was 13cm.