Question

29- If the volume and surface area of a
sphere are numerically equal then its radius
is.....(a) 2 units (b) 3 units (c) 4 units (d) 5
units​

Answer 1

Answer:

3

Step-by-step explanation:

its easy

(4/3)πr³=4πr²

(4/3)r=4

1/3r = 0

r=3

Answer 2

Answer:

$\bigstar{\bold{Option\:b:3\:units}}$

Step-by-step explanation:

$\Large{\underline{\underline{\bf{Given:}}}}$

• Volume of a sphere = Surface area of sphere

$\Large{\underline{\underline{\bf{To\:Find:}}}}$

• The radius of the sphere

$\Large{\underline{\underline{\bf{Solution:}}}}$

→ First we have to find the volume of the sphere.

→ Volume of a sphere is given by

→ Volume of a sphere = 4/3 × π × r³-----(1)

→ Now we have to find the surface area of the sphere

→ Surface area of a sphere is given by

  Surface area of a sphere = 4 π r²------(2)

→ By given we know that

  LHS of equation 1 and 2 are equal, hence RHS must also be equal.

  4/3 π r³ = 4 π r²

→ Cancelling 4 , π and r² on both sides

   1/3 r = 1

         r = 1 × 3

         r = 3 units

→ Hence the radius of the sphere is 3 units

$\boxed{\bold{Radius=3\:units}}$

→ Hence option b is correct

$\Large{\underline{\underline{\bf{Notes:}}}}$

→Volume of a sphere = 4/3 × π × r³

→  Surface area of a sphere = 4 π r²