MCQ
The radius of a sphere $($in $\ cm)$ whose volume is $12\pi \text{ cm}^3,$ is :
- A$3$
- B$3\sqrt{3}$
- ✓$3^{\frac23}$
- D$3^{\frac13}$
✓
Answer
Correct option: C.
$3^{\frac23}$
The volume of a sphere $=12\pi\text{ cm}^3$
Let the radius of a sphere $= r$
To find, the radius of a sphere $(r) = ?$
We know that,
The volume of a sphere $=\frac43\pi\text{r}^3$
According to question,
$\therefore\frac43\pi\text{r}^3=12\pi$
$\Rightarrow\text{r}^3=\frac{12\times3}{4}$
$\Rightarrow\text{r}^3=\frac{36}{4}$
$\Rightarrow\text{r}^3=9$
$\Rightarrow\text{r}=(3^2)^{\frac13}$
Using the identity,
$(\text{a}^{\text{m}})^{\text{n}}=\text{a}^{\text{mn}}$
$\Rightarrow\text{r}=3^{\frac23}\text{ cm}$
$\therefore$ The radius of a sphere $\text{(r)}=3^{\frac23}\text{ cm}$
Thus, the radius of a sphere $\text{(r)}=3^{\frac23}\text{ cm}$
Let the radius of a sphere $= r$
To find, the radius of a sphere $(r) = ?$
We know that,
The volume of a sphere $=\frac43\pi\text{r}^3$
According to question,
$\therefore\frac43\pi\text{r}^3=12\pi$
$\Rightarrow\text{r}^3=\frac{12\times3}{4}$
$\Rightarrow\text{r}^3=\frac{36}{4}$
$\Rightarrow\text{r}^3=9$
$\Rightarrow\text{r}=(3^2)^{\frac13}$
Using the identity,
$(\text{a}^{\text{m}})^{\text{n}}=\text{a}^{\text{mn}}$
$\Rightarrow\text{r}=3^{\frac23}\text{ cm}$
$\therefore$ The radius of a sphere $\text{(r)}=3^{\frac23}\text{ cm}$
Thus, the radius of a sphere $\text{(r)}=3^{\frac23}\text{ cm}$
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