| 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, |
| \[4\pi \,\,{{(r+2)}^{2}}=4\pi {{r}^{2}}+352\] |
| \[\Rightarrow \]\[4\pi \,\,{{(r+2)}^{2}}-4\pi {{r}^{2}}=352\] |
| \[\Rightarrow \]\[4\pi \,\,[{{(r+2)}^{2}}-{{r}^{2}}]=352\] |
| \[\Rightarrow \] \[4\pi \,\,[4+4r]=352\] |
| \[\Rightarrow \] \[(r+1)=\frac{352\times 7}{4\times 22\times 4}\] |
| \[\Rightarrow \]\[r+1=7\]\[\Rightarrow \]\[r=6\,\,cm\] |
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