AI Mentor

Check Your IQ

Free Expert Demo

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

Offline Centres

A rectangular sheet of paper $30 cm × 18 cm$ can be transformed into the curved surface of a right circular cylinder in two ways i.e., either by rolling the paper along its length or by rolling it along its breadth. Find the ratio of the volumes of the two cylinders thus formed.

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

4:2

5:3

7:2

4:9

answer is B.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

It is given a rectangular sheet of paper of size

30 cm × 18 cm

(Cylinder I)
By rolling lengthwise,
Height of cylinder

I (h 1) = 18

cm

Circumference of the cylinder

I = 30 cm

Since, the Circumference of the base of the cylinder is

2 π r

.
So,

2 π r 1 = 30

⇒ r 1 = 30 2 π

⇒ r 1 = 30 × 7 2 × 22

⇒ r 1 = 10522 c m

Volume

(V 1) = π r 1 2 h 1

V 1 = 227 × 10522 × 10522 × 18 c m 3

(Cylinder II)
By rolling breadthwise,
Height of cylinder II

(h 2)

= 30

cm

Circumference of cylinder II

= 18 cm

Since, the Circumference of the base of the cylinder is

2 π r

.
So,

2 π r 2 = 18

⇒ r 2 = 18 2 π

⇒ r 2 = 18 × 7 2 × 22

⇒ r 2 = 6322 cm

Volume

(V 2) = π r 2 2 h 2

V 2 = 227 × 6322 × 6322 × 30 c m 3

Divide

V 1

V 2

V 1 V 2 = 227 × 10522 × 10522 × 18 227 × 6322 × 6322 × 30

⇒ V 1 V 2 = 22 × 105 × 105 × 18 22 × 63 × 63 × 30

⇒ V 1 V 2 = 105 × 105 × 18 63 × 63 × 30

⇒ V 1 V 2 = 198450119070

⇒ V 1 V 2 = 53

Therefore, the Ratio of two cylinders is

5 : 3

.
Hence option (2) is correct.

Watch 3-min video & get full concept clarity

courses

No courses found

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Online Course for IIT JEE

Best Online Course for NEET

Best Online Course for CBSE

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Get Expert Academic Guidance – Connect with a Counselor Today!