Question

58 Given a solid cylinder of radius 10 cm and length
1000 cm, a cylindrical shell of uniform
thickness and having volume equal to one-fourth
of the original cylinder is made to cover the
cylinder. The thickness of the cylindrical shell is
:
एक ठोस बेलन जिसकी त्रिज्या और लम्बाई क्रमशः 10 सेमी और
1000 सेमी है। इससे ढ़कने के लिये एक बेलनाकार कवर
बनाया गया। जोकि, एक समान मोटाई का है और मूल बेलन के
आयतन के एक चौथाई आयतन का है। तब इस बेलनाकार कवर
की मोटाई बताओ।
(a)5(15-2) cm (b) 10(2-/3) cm
(d) 5/2cm
(c) 5cm
​

Answer 1

Answer:

Thickness of the cylindrical shell is 5 cm

Step-by-step explanation:

For the figure, refer to the attachment

Given,

Height of the cylinder (h) = 1000 cm

Radius of the cylinder (r) = 10 cm

We know that,

Volume of cylinder = πr²h

Using the above formula,

Volume of the cylinder = 1000 * 100 * π = 100000π cm³

Given that there is a cylindrical shell of uniform thickness inside the orginal cylinder whose volume is one-fourth of the volume of the original cylinder.

Let the radius of inner cylindrical shell be r the height of the inner cylindrical shell and the original cylinder is the same which is h = 1000 cm

Volume of the inner cylindrical shell = 1000r²π cm³

100000π/4 = 1000r²π

Cancelling π on both sides

100000/4 = 1000r²

r² = 100/4

r² = 25

r = ± 5cm

As radius is a physical quantity related to length, hence it can't be negative

r = 5 cm

Thickness of the cylindrical shell = R - r [R is the radius of the outer cylindrical shell andr is the radius of the inner cylindrical shell]

R = 10 cm

r = 5cm

Therefore,

Thickness of the cylindrical shell = 10 - 5 = 5 cm

$\boxed{\rm Thickness \: of \: the \: cylindrical \: shell \: is \: 5cm}$