CBSE Class 12-science Answered
Of all the closed cylindrical cans, which enclose a given volume has the minimum surface area?
Asked by | 07 Sep, 2009, 01:09: PM
Expert Answer
Given volume = V
πr2h = V
h = V/πr2
S = total surface area = 2πr2 + 2πrh
= 2πr2 + 2πr(V/πr2)
= 2πr2 + 2V/r
To minimize the surface area,
dS/dr = 4πr - 2V/r2 = 0
d2S/dr2 = 4π + 4V/r3 > 0
2πr = V/r2
r = (V/2π)1/3
r = (100/2π)1/3
r = 2.52 cm and h = 5.02 cm.
The cylindrical can with r = 2.52 cm and h = 5.02 cm, will minimize the total surface area.
Regards,
Team,
TopperLearning.
Answered by | 07 Sep, 2009, 01:44: PM
Application Videos
-
ProblemsbasedonIntoFunction-I
Video contains the question based on verification of a function to be Into ... -
ProblemsbasedonIntoFunction-II
Video contains the question based on verification of a function to be Into ...
Concept Videos
-
Properties of Inverse Trigonometry Part - 1
This video explains the properties of inverse trigonometric applications an... -
Graphical representation of inverse trigonometric funct ...
Graphical representation of inverse trigonometric functions and principle ... -
Continuous and Discontinuous function
Understand the meaning of function to be continuous and discontinuous, comb... -
Relationship between continuity and differentiability - ...
Relationship between continuity and differentiability, concept of composite... -
Introduction to Relations
This video explains the concept of relations and types of relation like Emp...
CBSE 12-science - Maths
Asked by mahammadsharifdakhani67 | 16 Apr, 2024, 07:43: PM
ANSWERED BY EXPERTCBSE 12-science - Maths
Asked by 20muskaansharma23 | 08 Apr, 2024, 11:31: AM
ANSWERED BY EXPERT
CBSE 12-science - Maths
Asked by cherrycharishma512 | 01 Apr, 2024, 12:32: PM
ANSWERED BY EXPERTCBSE 12-science - Maths
Asked by annapoornaa429 | 31 Mar, 2024, 08:23: PM
ANSWERED BY EXPERTCBSE 12-science - Maths
Asked by shirishakuruva477 | 28 Mar, 2024, 09:52: PM
ANSWERED BY EXPERTCBSE 12-science - Maths
Asked by sheensvlog | 27 Mar, 2024, 10:15: PM
ANSWERED BY EXPERTCBSE 12-science - Maths
Asked by jprathamesh023 | 23 Mar, 2024, 04:01: PM
ANSWERED BY EXPERTCBSE 12-science - Maths
Asked by antra1799 | 18 Mar, 2024, 07:49: PM
ANSWERED BY EXPERTCBSE 12-science - Maths
Asked by janusingh736 | 13 Mar, 2024, 04:19: PM
ANSWERED BY EXPERT
