GATE (TF) Textile 2010 Question Paper Solution | GATE/2010/TF/47

Question 47 (Textile Engineering & Fibre Science)

For a circular rod with volume 16\pi cm^3 the value of radius for which the surface area (including the top and bottom surfaces) will be minimum is

(A)1 cm
(B)2 cm
(C)3 cm
(D)4 cm
[Show Answer]

Volume=16\pi cm^3

As we know,

Volume of cylinder=\pi\times r^2 \times h

Where, r=radius and h is the height

\pi\times r^2 \times h=16\pi

r^2\times h=16


When surface area is minimum-

Surface area(S)=2\pi\times r \times h+2\pi\times r^2

S=2\pi\times r (r+h)

S=2\pi\times r (r+\frac{16}{r^2})

S=2\pi (r^2+\frac{16}{r})

Differentiate this with respect to r-

\frac{dS}{dr}=2\pi (2r-\frac{16}{r^2})=0



r=2 cm (Ans)

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