Answer :
∛128 is the radius r and height h of the cylinder with minimal surface area .
What is Surface Area?
- The term "area" refers to the area occupied by a flat, two-dimensional surface. In square units, it is calculated.
- A three-dimensional object's surface area is the space it takes up when viewed from the outside.
V = πr²n
128π = πr²n
n = 128/r²
s = 2πrn + 2πr²
s = 2πr 128/r² + 2πr²
s = 256π/r + 2πr²
ds/dt = - 256π/r² + 2πr
d²s/dt² = -256/(-2) r³ + 2π
d²s/dt² = 128/r³ + 2π
for maxima or minima
ds/dt = 0
- 256 π/r² + 2πr = 0
256 = 2r³
r = ∛128
d²s/dt² = 128/(∛128)³ + 2π
= 2π + 1
d²s/dt² > 0
so surface area is minimum
a + r = ∛128
n = 128(∛128)²
n = ∛128
r = ∛128 , n= ∛128
Learn more about surface area .
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