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 hollow cylinder having external radius 8 cm and height 10 cm has a total surface area of $338 π cm 2$ . Find the thickness of the hollow metallic cylinder.

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

2 cm

3 cm

4 cm

5 cm

answer is B.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

Given,
External radius 8 cm and height 10cm,
Total surface area

= 338 π c m 2

Let the internal radius of the hollow cylinder = r cm
Total surface area,

⇒ 2 π R + 2 π r + 2 π (R 2 − r 2) = 38 π

= 2 π (R h + r h + R 2 − r 2) = 338 π → (1)

⇒ (10 × 8) + (10 × r) + (8) 2 − r 2 = 338 π 2 π

⇒ (80) + (10 r) + 64 − r 2 = 169 ⇒ − r 2 + 10 r = 169 − 144 ⇒ − r 2 + 10 r = 25 → (2)

⇒ r 2 − 10 r + 25 = 0

⇒ r 2 − (5 + 5) r + 25 = 0 ⇒ r 2 − 5 r − 5 r + 25 = 0 ⇒ r (r − 5) − 5 (r − 5) = 0

⇒ (r − 5) = 0 ⇒ r = 5

Now as we know the thickness of a hollow cylinder can be obtained by subtracting the inner radius which is r from the outer radius which is R as given in the solution hint. Therefore
The thickness of the metal

When substituting the values in the above expression

⇒ 8 − 5 = 3 c 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!