Answer:
h = 5.42
r = 5.42
Step-by-step explanation:
Find h with respect to r:
V = πr²h = 500
h = 500/πr²
Plug this into the surface area equation:
SA = πr² + 2πrh
= πr² + 2πr(500/πr²)
= πr² + 1000/r
Differentiate and set to 0, solve for r:
dSA/dr = 2πr - 1000/r² = 0
2πr = 1000/r²
r³ = 500/π
r = (500/π)^1/3
≈ 5.42 cm
find h:
h = 500/πr²
= 500/[π(5.42)²]
= 5.42cm
