Question

The volume of the sphere is StartFraction 500 Over 3 EndFractionπ cubic units. A sphere has a radius of x units. What is the value of x? 4 units 5 units 8 units 10 units

Answer 1

5 units

Explanation:

Answer 2

(b) Radius of the sphere = 5 units.

Explanation:

Here, given:

The volume of the sphere =
`((500)/(3))\pi` cubic units ... (1)

Also, radius of the sphere = x units

Now, VOLUME OF SPHERE =
`((4)/(3)) \pi r^3`

So, volume of a sphere with radius x =
`((4)/(3)) \pi (x)^3`

But volume of sphere is given by (1).

`\implies ((500)/(3))\pi = ((4)/(3)) \pi (x)^3\\\implies ((500)/(3)) = ((4)/(3)) (x)^3\\\implies x^3 = ((500)/(3))  * ((3)/(4))  = 125\\\implies x^ 3 = 125 = (5)^3\\\implies x  = 5`

Hence, radius of the sphere = 5 units.