A rectangular sheet of fixed perimeter with sides having their lengths in the ratio 8 : 15 is converted into an open rectangular box by folding after removing squares of equal area from all four corners. If the total area of removed squares is 100, the resulting box has maximum volume. The lengths of the sides of the rectangular sheet are
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
(a,c)
Let λ = 8x, b = 15 x
∴ Volume = (8x – 2a) (15x – 2a) = 4a 3 – 46a 2 x + 120 ax 2
= 6a 2 – 46ax + 60 x 2
= 0
∴ x = 3 and 
= 6a – 23x
< 0,
So, at x = 3 gives maxima
> 0
So, at x = 
gives minima.
= 0 when a = 5 given ( ∴ 4a 2 = 100 given for maximum volume)
at a = 5
by 
= 0
⇒ 6x 2 – 23x + 15 = 0
x = 3 or 5/6
So by x = 3 (for max volume)
8x = 24, 15x = 45
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