 ×     #### Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Click to Chat

1800-1023-196

+91-120-4616500

CART 0

• 0

MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping
```
. Find the dimensions of the rectangle of perimeter 36 cm which will sweep out a volume as large as possible, when revolved about one of its sides. Also find the maximum volume.

```
one month ago Anand Kumar Pandey
1652 Points
```							Dear studentLet’s consider x and y to be the length and breadth of given rectangle ABCD.According to the question, the rectangle will be resolved about side AD which making a cylinder with radius x and height y.So, the volume of the cylinder V =π r^2 h =π x^2 y.... (1)Now, perimeter of rectangle P = 2(x + y)36 = 2(x + y)18 = x + yy = 18–x..... (ii)Putting the value of y in the equation (i), V =π x^2 (18–x)=π(18x^2–x^3)Differentiating both sides w.r.t. xdV/dx =π(36x–3x^2)................ (iii)For local maxima and local minima dV/dx =  π(36x–3x^2) = 036x–3x^2=03x(12 - x) = 0x≠0 and 12–x = 0⇒x = 12From equation (ii), we havey = 18–12 = 6Differentiating equation (iii) w.r.t. x, we getd^2V/dx^2= π(36–6x)At x = 12,d^2 V/dx^2=π(36–6 x 12) =π(36–72) = -36π< 0 maximaNow, volume of the cylinder so formed =π x^2 y=πx (12)^2x (6)=π(144)^2x 6= 864πcm^3Therefore, the required dimension are 12 cm and 6 cm and the maximum volume is 864πcmThanks
```
one month ago
Think You Can Provide A Better Answer ?

## Other Related Questions on Differential Calculus

View all Questions »  ### Course Features

• 731 Video Lectures
• Revision Notes
• Previous Year Papers
• Mind Map
• Study Planner
• NCERT Solutions
• Discussion Forum
• Test paper with Video Solution  ### Course Features

• 51 Video Lectures
• Revision Notes
• Test paper with Video Solution
• Mind Map
• Study Planner
• NCERT Solutions
• Discussion Forum
• Previous Year Exam Questions