The rectangle of perimeter 36 cm is revolved about one side to form a cylinder of maximum volume. The length and breath of the rectangle are in the ratio.

1 : 1

No worries! We‘ve got your back. Try BYJU‘S free classes today!

1 : 3

No worries! We‘ve got your back. Try BYJU‘S free classes today!

2 : 3

No worries! We‘ve got your back. Try BYJU‘S free classes today!

2 : 1

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is C 2 : 1
Perimeter $= 2 (a + b)$
$a + b = 18$
$2 π r = a$
$b = h$
Volume of cylinder $= π r^{2} h$
$= π \frac{a^{2}}{4 π^{2}} b$
$\frac{d v}{d a} = \frac{1}{4 π} (2 a (18 - a) - a^{2})$
$0 = a (36 - 3 a)$
$a = 12$ $b = 6$
$a : b = 2 : 1$

Suggest Corrections

Similar questions

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.

Q. 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.

Q. A rectangle of perimeter

36 c m

swept maximum possible volume, when it is revolved about one of its sides. Then which of the following is/are true

A rectangle of length “a” and breadth “b” is revolved $360^{\circ}$ about its length. The volume of the resulting cylinder is

Q. The ratio of length and breadth of a rectangle is

3 : 1

and its perimeter is

36

cm. Find the length and breadth of the rectangle.

Join BYJU'S Learning Program

The rectangle of perimeter 36 cm is revolved about one side to form a cylinder of maximum volume. The length and breath of the rectangle are in the ratio.

The correct option is C 2 : 1Perimeter=2(a+b)a+b=182πr=ab=hVolume of cylinder =πr2h=πa24π2bdvda=14π(2a(18−a)−a2)0=a(36−3a)a=12 b=6a:b=2:1

The correct option is C 2 : 1
Perimeter $= 2 (a + b)$
$a + b = 18$
$2 π r = a$
$b = h$
Volume of cylinder $= π r^{2} h$
$= π \frac{a^{2}}{4 π^{2}} b$
$\frac{d v}{d a} = \frac{1}{4 π} (2 a (18 - a) - a^{2})$
$0 = a (36 - 3 a)$
$a = 12$ $b = 6$
$a : b = 2 : 1$