Book Online Demo

Check Your IQ

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 well with 14 m diameter is dug 8 m deep. The earth taken out of it has been evenly spread all around it to a width of 21 m to form an embankment. Find the height of the embankment.

see full answer

High-Paying Jobs That Even AI Can’t Replace — Through JEE/NEET

🎯 Hear from the experts why preparing for JEE/NEET today sets you up for future-proof, high-income careers tomorrow.

An Intiative by Sri Chaitanya

53 cm

54 cm

64 cm

73 cm

answer is A.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

It is given a well of diameter 14 m and depth 8 m, width of the embankment is 21 m.
Given, Question Image

Since, radius=

D i a m e t e r 2

So, radius(r) ,

⇒ r = 142 ⇒ r = 7 m

Volume =

π r 2 h

V = 227 × 72 × 8

⇒ V = 227 × 7 × 7 × 8

⇒ V = 1232 m 3

Now, width of embankment = 21 m
Inner radius = Radius of a cylindrical well = 7m
Outer radius = Width of embankment + Radius of cylindrical well

⇒

Outer radius = 21m+7m

⇒

Outer radius = 28m
Since, area of the material contained in a hollow cylindrical shell =

π R 2 − r 2

So, area of the embankment,

A r e a o f t h e e m b a n k m e n t = π R 2 − r 2

⇒ A r e a o f t h e e m b a n k m e n t = 227 282 − 72

⇒ A r e a o f t h e e m b a n k m e n t = 227 28 + 7 28 − 7

⇒ A r e a o f t h e e m b a n k m e n t = 227 × 35 × 21

⇒ A r e a o f t h e e m b a n k m e n t = 2310 m 2

Since, volume of the embankment = Area of embankment

×

Height of embankment

⇒ V o l u m e o f t h e e m b a n k m e n t = π R 2 − r 2 h

And volume of embankment = Volume of the earth that dugout = 1232

m 3

So, height of embankment =

V o l u m e o f e m b a n k m e n t A r e a o f e m b a n k m e n t

H e i g h t o f e m b a n k m e n t = 12322310 ⇒ H e i g h t o f e m b a n k m e n t = 0.53 m

We know that, 1m = 100

cm

So, 0.53m = 53cm
Therefore, the height of the embankment is 53

cm

.
Hence option (1) is correct.

Watch 3-min video & get full concept clarity

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!

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