Question

The radius of a sphere (in cm) whose volume is 12πcm³, is
A) 3
B) 3√3
C) 3⅔
D) 3⅓

Answer 1

Answer: option c is correct that is 3^2/3

Answer 2

The required "option C) $3^{\dfrac{2}{3}}$ " is correct.

Step-by-step explanation:

Let the radius of a sphere = r

The volume of a sphere = 12π $cm^{3}$

To find, the radius of a sphere (r) = ?

We know that,

The volume of a sphere = $\dfrac{4}{3} \pi r^3$

According to question,

$\dfrac{4}{3} \pi r^3$ = 12π

⇒ $r^3$ = $\dfrac{12\times 3}{4}$

⇒ $r^3$ = $\dfrac{36}{4}$

⇒ $r^3$ = 9

⇒ $r^3$ = $3^2$

⇒ r = $(3^2)^{\dfrac{1}{3}}$

Using the identity,

$(a^m)^{n}=a^{mn}$

⇒ r = $3^{\dfrac{2}{3}}$ cm

∴ The radius of a sphere (r) = $3^{\dfrac{2}{3}}$ cm

Thus, the required "option C) $3^{\dfrac{2}{3}}$ " is correct.