algebra story problem

Question

the volume of a sphere with radius r is V=4/3πr^3. spaceship earth at epcot center in Florida is approximately a sphere with a volume of 62,000m^3. Find its radius to the nearest meter.

Answer 1

V=(4/3)(∏)(r³)

62,000=(4/3)(∏)(r³)

multiply both sides by 3/4

46,500=∏(r³)

(46,500/∏)=r³

take the cube root of both sides

(46,500/∏)^(1/3)=r

factor 46,500

46,500=5*3*31*2*2*5*5=2*2*3*31*5³

the cube root of 5³ is 5

5[(2*2*3*31)/∏]^(1/3)=r

5[(372/∏)^(1/3)]=r is the exact answer

you want r to the nearest meter

5(118.41138)^(1/3)=r

the cube root of 118.41138 is 4.91056142067

5*4.91056142067=24.552807

r=24.552807 meters

r=25 meters to the nearest meter