Answer :

1. The formula of the Volume of a sphere is V(r)=[tex] \frac{4}{3} \pi r^{3} [/tex]

2. the radius is x, and the resulting volume is [tex] \frac{500}{3} \pi [/tex] [tex] units^{3} [/tex]

3. [tex] \frac{4}{3} \pi x^{3} =\frac{500}{3} \pi [/tex]

multiply both sides by 3 and divide them by [tex] \pi [/tex]:

[tex]4 x^{3} =500[/tex]

[tex]x^{3} = \frac{500}{4}= \frac{250}{2}=125 [/tex]

[tex]x= \sqrt[3]{125}=5 [/tex] (units)

scme1702
The volume of a sphere is given by:
4/3 * πr³
From the figure, we can see that x is the radius of the sphere. Therefore, we may substitute x in the formula for volume and equate it to the given volume as follows:
500π/3 = 4/3 * πx³
4x³ = 500
x = 5

The value of x is 5 units

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