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Question

The total surface area of a hollow cylinder which is open from both sides is $$4620$$ sq. cm, area of base ring is $$115.5$$ sq. cm and height $$7$$ cm. Find the thickness of the cylinder.


Solution

Let the inner and outer radii of hollow cylinder be r cm and R cm respectively. Then,
$$2\pi h+2\pi Rh+2\pi R^2-2\pi r^2=4620$$ …….(i)
and, $$\pi R^2-\pi r^2=115.5$$ …….(ii)
$$\Rightarrow 2\pi h(r+R)+2(\pi R^2-\pi r^2)=4620$$ and, $$\pi R^2-\pi r^2=115.5$$
$$\Rightarrow 2\pi h(r+R)+2\times 115.5=4620$$ and $$\pi(R^2-r^2)=115.5$$
$$\Rightarrow 2\pi\times 7(r+R)=4389$$ and $$\pi(R+r)(R-r)=115.5$$
$$\Rightarrow \pi(R+r)=313.5$$ and $$\pi(R+r)(R-r)=115.5$$
$$\Rightarrow \dfrac{\pi(R+r)(R-r)}{\pi(R+r)}=\dfrac{115.5}{313.5}$$
$$\Rightarrow R-r=\dfrac{7}{19}$$cm.

Mathematics

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