MCQ
If the surface area of a sphere is $(144\pi)\text{m}^2$ then its volume is:
- A$(288\pi)\text{m}^3$
- ✓$(188\pi)\text{m}^3$
- C$(300\pi)\text{m}^3$
- D$(316\pi)\text{m}^3$
✓
Answer
Correct option: B.
$(188\pi)\text{m}^3$
Given that surface area of a sphere $=144\pi\text{m}^2$
$\Rightarrow4\pi\text{r}^2=144\pi$
$\Rightarrow4\times\text{r}^2=144$
$\Rightarrow\text{r}^2=\frac{144}{4}$
$\Rightarrow\text{r}^2=36$
$\Rightarrow\text{r}=6\text{ cm}$
Volume of sphere $=\frac{4}{3}\pi\text{r}^3$
$=\frac{4}{3}\times\pi\times6\times6\times6$
$=4\times\pi\times2\times6\times6$
$=288\pi\text{m}^3$
$\Rightarrow4\pi\text{r}^2=144\pi$
$\Rightarrow4\times\text{r}^2=144$
$\Rightarrow\text{r}^2=\frac{144}{4}$
$\Rightarrow\text{r}^2=36$
$\Rightarrow\text{r}=6\text{ cm}$
Volume of sphere $=\frac{4}{3}\pi\text{r}^3$
$=\frac{4}{3}\times\pi\times6\times6\times6$
$=4\times\pi\times2\times6\times6$
$=288\pi\text{m}^3$
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