MCQ
The surface area of a sphere is $1386\ cm^2.$ Its volume is:
- A$1617\ cm^3$
- B$3234\ cm^3$
- ✓$4851\ cm^3$
- D$9702\ cm^3$
✓
Answer
Correct option: C.
$4851\ cm^3$
Given surface area of a sphere $= 1386\ cm^2$
$\Rightarrow4\pi\text{r}^2=1386$
$\Rightarrow4\times\frac{22}{7}\times\text{r}^2=1386$
$\Rightarrow\frac{88}{7}\times\text{r}^2=1386$
$\Rightarrow\text{r}^2=\frac{1386\times7}{88}$
$\Rightarrow\text{r}^2=\frac{441}{88}$
$\Rightarrow\text{r}=\sqrt{\frac{441}{4}}$
$\Rightarrow\text{r}=\frac{21}{2}\ cm$
Volume of sphere $=\frac{4}{3}\pi\text{r}^3$
$=\frac{4}{3}\times\frac{22}{7}\times\frac{21}{2}\times\frac{21}{2}\times\frac{21}{2}$
$=11\times21\times21$
$=4851\ cm^3$
$\Rightarrow4\pi\text{r}^2=1386$
$\Rightarrow4\times\frac{22}{7}\times\text{r}^2=1386$
$\Rightarrow\frac{88}{7}\times\text{r}^2=1386$
$\Rightarrow\text{r}^2=\frac{1386\times7}{88}$
$\Rightarrow\text{r}^2=\frac{441}{88}$
$\Rightarrow\text{r}=\sqrt{\frac{441}{4}}$
$\Rightarrow\text{r}=\frac{21}{2}\ cm$
Volume of sphere $=\frac{4}{3}\pi\text{r}^3$
$=\frac{4}{3}\times\frac{22}{7}\times\frac{21}{2}\times\frac{21}{2}\times\frac{21}{2}$
$=11\times21\times21$
$=4851\ cm^3$
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