#" "#
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.
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.