Question

The radius of sphere whose volume is 12πcm^3.,is
(A) 3
(B) 3√3
(C) 3^2÷3
(D) 3^1÷32

Answer 1

The radius of sphere whose volume is 12πcm^3 is  ∛9 cm (2.08 cm)

It is given that a sphere has a volume of 12П cm³.

We know that for a sphere of radius 'r', its volume if given as:

V = (4/3)*Пr³.

Here, let the radius be 'r' cm.

So, volume is = (4/3)*Пr³

Thus, (4/3)*Пr³ = 12П

⇒ (4/3)*r³ = 12

⇒ r³ = 12*3/4 = 9

⇒ r = ∛9 cm

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.