Question

The area of the sphere ${\left|\overrightarrow{r}\right|}^2+\overrightarrow{r}(\widehat{2i}+\widehat{4j}-\widehat{2k})=10$ is

• A. $4\pi$ sq. units
• B. $16\pi$ sq. units
• C. $64\pi$ sq. units
• D. $128\pi$ sq. units

Answer 1

Answer: (C)

$64\pi$ sq. units

For a sphere ${\overline{r}}^2+\overline{r}(2g\hat{i}+2f\hat{j}+2h\hat{k})+c=0$, the radius is given by $\sqrt{g^2+f^2+h^2-c}$
The radius of the sphere here becomes $r=\sqrt{1+4+1+10}=4$ units.
Thus, area $=4\pi r^2=64\pi$ sq. units,