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 copper sphere has an 18 cm diameter. It is then heated and pulled into a length of wire with a consistent cross section. Find the diameter of the wire if its length is 108 m.

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

0.5 cm

0.6 cm

0.7 cm

0.8 cm

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 the sphere is 18 cm in diameter.

∴ d = 18 cm ⇒ r = 9 cm

Also, given that the wire is 108 m long.

∴ h = 108 m = 10800 c m

We know that the volume of the sphere is

43 π r 3,

where r is its radius.
The volume of a cylinder is

π r 2 h,

where r is the radius of the base and h is the cylinder's height.
Let’s assume that the radius of the wire is

R .

∴ 43 π × r 3 = π × R 2 × 10800 ⇒ 43 π × 93 = π × R 2 × 10800

⇒ R 2 = 43 π × 729 π × 10800 ⇒ R = 9100 ⇒ R = 0.3 cm

Therefore the diameter of the wire can be calculated as,
Question Image

Therefore the wire has a 0.6 cm diameter.
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!