The radius needed to create a sphere with a given volume V can be approximated by the equation
r = 0.6(V)^1/3. Find the radius of a sphere with a volume of 729 cubic meters. Round the answer to the nearest hundredth.
V = (4/3) pi r^3
= 4.189 r^3
so
r = V^(1/3)/(4.189)^(1/3)
r = .620 V^(1/3) I thought they were off a bit.
Ok, using r = .6 V^(1/3)
r = .6 *729^(1/3)
r = .6 * 9
r = 5.40 meters
To find the radius of a sphere with a volume of 729 cubic meters using the formula r = 0.6(V)^(1/3), we can substitute the given volume value into the equation.
Step 1: Substitute the value of V into the formula:
r = 0.6(729)^(1/3)
Step 2: Evaluate the exponent:
r = 0.6 × (729)^(1/3)
r = 0.6 × 9
Step 3: Calculate the result:
r = 5.4
Step 4: Round the answer to the nearest hundredth:
Rounded to the nearest hundredth, the radius is 5.40 meters.