Math, asked by suraboinaganesh, 9 months ago

A right circular of volume 1386 cm is cut from a right
circular cylinder of radius 4 cm and height 49 cm, such that
a hollow cylinder of uniform thickness, with a height of 49
cm and an outer raidus of 4 cm is left behind. Find the
thickness of the hollow cylinder left behind. आयतन 1386
cm का एक सही गोलाकार त्रिज्या 4 सेमी और ऊँचाई 49 सेमी के एक दाएँ
परिपत्र सिलेंडर से काटा जाता है, जैसे कि 49 सेमी की ऊँचाई के साथ एक
समान मोटाई का एक खोखला सिलेंडर, और 4cm का बाहरी आवरण पीछे
रह गया है। पीछे छोड़े खोखले सिलेंडर की मोटाई का पता लगाएं।
3

Answers

Answered by Anonymous

0.5 cm

2 cm

1.5 cm

1 cm

Answer:

Solution :

Find the radius of the cylinder which is cut. (i.e., trh

1386).

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Answered by Afreenakbar

The thickness of the hollow cylinder left behind is 0.6cm.

The volume of the right circular cylinder is given by the formula: $V = \pi r^2h$

The volume of the right circular cylinder is 1386 cm^3, the radius is 4 cm and the height is 49cm, so we can substitute these values into the formula:

$1386 = \pi (4^2)h$

We can solve for h:

1386 = 16πh

h = 1386 / 16π = $1386 / (16 * 3.14) = 49$

We know that the height of the cylinder is 49cm and the radius of the cylinder is 4cm, so the original cylinder has a volume of:

V = $\pi r^2h = \pi (4^2) * 49 = 3.14 * 16 * 49 = 3136 cm^3$

The volume of the hollow cylinder is the volume of the original cylinder minus the volume of the removed cylinder:

Vhollow = Voriginal - Vremoved = 3136 - 1386 = $1750 cm^3$

We know that the height of the hollow cylinder is 49cm and the radius of the hollow cylinder is 4cm, so we can use the formula of the volume of a cylinder to find the radius of the inner cylinder :

Vhollow = $\pi (r_i^2)h$

Where r_i is the radius of inner cylinder

$r_i = \sqrt(Vhollow / (\pi * h)) = \sqrt(1750 / (3.14 * 49)) =\ \sqrt(1750 / 151.86) = \sqrt(11.51) = 3.4 cm$

So the thickness of the hollow cylinder is 4cm - 3.4cm = 0.6 cm

Therefore the thickness of the hollow cylinder left behind is 0.6cm.