If a sphere has a volume of 3487 cubic yards whats the radius?

1 Answer
Apr 27, 2018

#" "#
Radius of the Sphere #~~color(red)(" 9.4 yards"#

Explanation:

#" "#
Volume of a Sphere (V) Formula: #color(blue)((4/3) * pi * r^3#

Given: #color(brown)(Volume (V) = "3487 Cubic yards"#

Find the Radius (r) using the formula.

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Substitute the values known:

#3487=(4/3)*pi*r^3#

Mathematical Constant #color(blue)(pi# has an approximate value of 3.14159

#rArr 3487 = (4/3)*3.14159*r^3#

Switch sides:

#rArr (4/3)*3.14159*r^3 = 3487#

Divide both sides by #4/3#

#rArr [(4/3)*3.14159*r^3]/(4/3) = 3487/(4/3)#

Simplify:

#rArr [cancel(4/3)*3.14159*r^3]/cancel(4/3) = 3487/(4/3)#

#rArr 3.14159*r^3 = 3487/(4/3)#

Divide both sides by #3.14159#

#rArr (3.14159*r^3)/3.14159 = 3487/((4/3)*3.14159)#

Simplify:

#rArr [(cancel(3.14159)*(r^3))/cancel3.14159] = 3487/((4/3)*3.14159)#

#rArr r^3 = 3487/((4/3)*3.14159)#

Using calculator:

#r^3 ~~ 3487/4.188790205 #

#r^3 ~~ 832.45993#

#r~~832.45993^(1/3)#

Using a calculator:

#r~~ 9.407071523#

Hence,

Radius of the Sphere #~~color(red)(" 9.4 yards"#

Hope it helps.