A cylindrical container is to be made from certain solid material with the following constraints: It has fixed inner volume of V mm 3 , has a 2 mm thick solid wall and is open at the top. The bottom of the container is solid circular disc of thickness 2 mm and is of radius equal to the outer radius of the container.
If the volume of the material used to make the container is minimum when the inner radius of the container is 10 mm, then the value of 
is
Text Solution
Verified by Experts4
(4)
Volume of material V = π r 2 h
⇒ V 1 = π (r + 2) 2 2 + π (r + 2) 2 h – π r 2 h ⇒ V 1 = 2 π (r + 2) 2 + π h(4 + 4r)
⇒ V 1 = 2 π (r + 2) 2 + 4 π h(r + 1) ⇒ V 1 = 2 π 
⇒ 
⇒ 
⇒ 
⇒ v = 10 3 π ⇒ 
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems