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

2/3 yards or 2 feet

Step-by-step explanation:

The formula for the volume of a sphere is , meaning that you can set up the following equation:

Divide both sides by :

Take the cube root of both sides:

yards. Hope this helps!

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 ]

x = central angle apc = measure of minor arc ac

the two angles x and 30 add to 180, so x+30 = 180 and x = 180-30 = 150. the measure of minor arc ac is 150 degrees.

what we need to do from here is find the circumference and then multiply it by x/360 since there are 360 degrees in a circle. in this case, x = 150, so x/360 = 150/360 = 15/36 = 5/12. the shortest distance along the curve from a to c is 5/12 of the distance around the entire circle (aka circumference)

c = circumference

c = pi*d

c = pi*24

c = 24pi

now multiply this by 5/12 to get

distance along minor arc ac = (5/12)*(circumference)

distance along minor arc ac = (5/12)*(24pi)

distance along minor arc ac = 10pi

the formula you can use is

l = (x/360)*pi*d

with

l = length of minor arc

x = central angle

d = diameter

which essentially is the steps we took though a bit differently.

hope it you

step-by-step explanation:

sin(7pi/6 - pi/3)  

= sin(7pi/6 - 2pi/6)  

= sin(5pi/6)  

= sin(pi - pi/6)  

= sin(pi/6)  

= 1/2  

sin 7pi/6 - sin pi/3  

= sin (pi + pi/6) - sin pi/3  

= -sin pi/6 - sin pi/3  

= -1/2 - sqrt(3)/2  

= -(1+sqrt(3))2