TS EAMCET · Maths · Application of Derivatives
A right solid circular cylinder of given volume will have the least total surface area when
- A its height is equal to its radius.
- B its height is equal to its diameter.
- C its height is independent of its radius.
- D its height is times of its radius.
Answer & Solution
Correct Answer
(B) its height is equal to its diameter.
Step-by-step Solution
Detailed explanation
Let the height of R.C. solid cylinder be h. Let the radius of it be r. So, its volume V=πr2h⇒h=Vπr2 ...i Again, total surface area S=2πrh+2πr2 ⇒S=2πr·Vπr2+2πr2 S=2Vr+2πr2 Differentiating w.r.t. r, we get…
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