Question

Find the radius of the sphere with a volume of 32/81π cubic yards. Write your answer as a fraction in simplest form.

Answer 1

Answer:

Step-by-step explanation:

The formula for the volume of a sphere of radius r is   V = (4/3)(π)r^3.  

Here we know the volume is V = (32/81)πr^3, but want to find the radius.

                                                                                V

Solving the above formula for r^3, we get  -----------------

                                                                           (4/3)(π)                  

                                                         32(π)  

and so, with V = (4/3)(π)r^3,   r^3 = ----------

                                                             81

The radius of the sphere is the cube root of the above equation:

r = ∛ [(32(π)  / 81 ]

Answer 2

Answer:

2/3 yards or 2 feet

Step-by-step explanation:

The formula for the volume of a sphere is $\frac{4}{3}\pi r^3$, meaning that you can set up the following equation:

$\dfrac{32\pi}{81}=\dfrac{4}{3}\pi r^3$

Divide both sides by $\frac{4}{3}\pi$:

$\dfrac{8}{27}=r^3$

Take the cube root of both sides:

$r=\dfrac{2}{3}$ yards. Hope this helps!