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 wooden pencil with an inner diameter of 0.50 cm is filled with lead of volume $2.2 dm 3 .$

The manufactured pencil will be of the length

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

110 m

112 m

98 m

12 m

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 that a wooden pencil with an inner diameter of 0.50 cm is filled with lead of volume

2.2 dm 3 .

We know that

1 dm = 10 cm

.
That is,

2.2 × 1000 = 2200 cm 3

lead is to be drawn into a cylindrical shape.
Since the diameter of the cylinder is 0.50 cm, so its radius will be,

r = 0.50 2 = 0.25 cm .

Let the height of the pencil is h cm.
Since all of the lead needs to be inserted into the pencil, therefore,
Lead volume = Volume of the cylinder.
Volume of a cylinder =

π r 2 h,

where r is the radius and h is the height of the cylinder.

∴ π r 2 h = 2200 ⇒ 227 × 0.25 × 0.25 × h = 2200 ⇒ h = 11200 cm ⇒ h = 112 m ∵ 100 cm = 1 m

Therefore the height of the manufactured pencil will be 112 m.
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!