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Andrew [12]
3 years ago
12

Find the dimensions of a closed right circular cylindrical can of smallest surface area whose volume is 128pi cm^3

Mathematics
1 answer:
Ratling [72]3 years ago
4 0
The surface area of a cylindrical can is equal to the sum of the area of two circles and the body of the cylinder: 2πr2 + 2πrh. volume is equal to π<span>r2h.

V = </span>π<span>r2h = 128 pi
r2h = 128 
h = 128/r2

A = </span><span>2πr2 + 2πrh
</span>A = 2πr2 + 2πr*(<span>128/r2)
</span>A = 2πr2 + 256 <span>π / r
</span><span>
the optimum dimensions is determined by taking the first derivative and equating to zero.

dA = 4 </span>πr - 256 <span>π /r2 = 0
r = 4 cm
h = 8 cm
</span><span>

</span>
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