Question

what is the radius of the sphere whose surface area is numerically equal to its volume​

Answer 1

Hey!

• Given : Surface area = Volume

• We know that, Surface area of a sphere = 4πr²

and volume of a sphere = 4/3πr³

Now, comparing the values.

• 4πr² = 4/3πr³

• 4πr²*3 = 4πr³

Therefore, radius = 3

Hope it helps!

Answer 2

Answer:

radius = 3  unit

Step-by-step explanation:

Surface area of sphere = 4πr²

Volume of sphere = (4/3) πr³

Let these be same(numerically) for radius = R.

  ⇒ Surface area = volume

⇒ 4πr² = (4/3) πr³

⇒ r² = r³/3

⇒ 3r² = r³

⇒ 3r² - r³ = 0

⇒ r²(3 - r) = 0

    r² = 0       or  3 - r = 0

    r = 0         or    r = 3