Find the radius of a sphere with a volume of 121.5π

cubic feet.

Answer: 4.5ft

Step-by-step explanation:

The volume of a sphere = 4/3πr³

This is question on solid shapes.

Since the volume of the sphere = 121.5πft³ meaning that π was not defined.

Now to get the radius of the sphere, we equate the formula above to the value and now solve for r making it the subject of the formula.

(4/3) πr³ = 121.5π

Now we shall try and make the equation a linear expression by multiplying through by 3 which is the denominator. It now becomes

4πr³ = 121.5π x 3

4πr³ = 364.5π

Now we divide through by π because it is common,

4r³ = 364.5, again divide by 4,

r³ = 91.125, now to find the true r, we take the cube root of both side, (recall, laws of indicies)

r = 3√91.125

= 4.5ft.

Therefore the radius of the sphere is 4.5ft.