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

Mathematics

2 answers:

kotykmax [81]2 years ago

6 0

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.

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 = ----------

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

r = ∛ [(32(π) / 81 ]

Vilka [71]2 years ago

3 0

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!

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yuradex [85]

What is the question??

3 0

2 years ago

#82 will give brainliest to best answer!

Fofino [41]

Answer:

$\frac{6}{k-6}$

Step-by-step explanation:

First, we can factor all of the following equations to turn that weird, huge looking thing into $\frac{(k+6)(k-6)}{(k-6)(k-10)}$ ÷ $\frac{(k-6)^2}{k(k-6)}$ × $\frac{6(k-10)}{k(k + 6)}$ . We know that division is simply multiplication by the reciprocal, so that whole equation will turn into $\frac{(k+6)(k-6)}{(k-6)(k-10)}$ × $\frac{k(k-6)}{(k-6)^2}$ × $\frac{6(k-10)}{k(k+6)}$ . Now we can cancel out some values if they are both in the numerator and denominator, which will turn that still huge looking thing into $\frac{6}{k-6}$ which is our final answer, as it cannot be simplified further.