Question

find the radius of a sphere in cm whose volume is 12π cm3

Answer 1

Step-by-step explanation:

The volume of a sphere = 12π cm^{3}cm

3

Let the radius of a sphere = r

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

Solution:

We know that,

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

3

4

πr

3

According to question,

∴ \dfrac{4}{3} \pi r^3

3

4

πr

3

= 12π

⇒ r^3r

3

= \dfrac{12\times 3}{4}

4

12×3

⇒ r^3r

3

= \dfrac{36}{4}

4

36

⇒ r^3r

3

= 9

⇒ r^3r

3

= 3^23

2

⇒ r = (3^2)^{\dfrac{1}{3}}(3

2

)

3

1

Using the identity,

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

m

)

n

=a

mn

⇒ r = 3^{\dfrac{2}{3}} cm3

3

2

cm

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

3

2

cm

Thus, the radius of a sphere (r) = 3^{\dfrac{2}{3}}3

3

2

cm

Answer 2

Volume of Sphere = 4/3 π r³

here volume is 12 π cm³

∴ 4/3 π r³ = 12 π cm³

∴ 4 r³ = 36

∴  r³ = 9

∴  r = 3∧(2/3)