If the radius of the sphere is increased by 2 cm, its surfaces area increases by \[352\,\,c{{m}^{2}}.\] The radius of the sphere before increase was |
A) 3 cm
B) 4 cm
C) 6 cm
D) 6 cm
Correct Answer: D
Solution :
Let the radius of the sphere be r cm. |
Then, surface area of sphere \[=4\pi {{r}^{2}}\] |
According to the question, |
\[4\pi \,\,{{(r+2)}^{2}}=4\pi {{r}^{2}}+352\] |
\[\Rightarrow \]\[4\pi \,\,{{(r+2)}^{2}}-4\pi {{r}^{2}}=352\] |
\[\Rightarrow \]\[4\pi \,\,[{{(r+2)}^{2}}-{{r}^{2}}]=352\] |
\[\Rightarrow \] \[4\pi \,\,[4+4r]=352\] |
\[\Rightarrow \] \[(r+1)=\frac{352\times 7}{4\times 22\times 4}\] |
\[\Rightarrow \]\[r+1=7\]\[\Rightarrow \]\[r=6\,\,cm\] |
You need to login to perform this action.
You will be redirected in
3 sec