The total surface area of a hollow cylinder which is open on both the sides is 4620 sq.

Solution:

Let the inner radius of the hollow cylinder be r1 cm

The outer radius of the hollow cylinder be r2 cm

Then,

$2 \pi r_{1} * h+2 \pi r_{2} * h+2 \pi r_{2}^{2}-2 \pi r_{1}^{2}=4620 \ldots$ (a)

$\pi r_{1}^{2}-\pi r_{2}^{2}=115.5 \ldots$

Now solving eq (a)

$2 \pi r_{1} h+2 \pi r_{2} h+2 \pi r_{2}^{2}-2 \pi r_{1}^{2}=4620$

$\Rightarrow 2 \pi h\left(r_{1}+r_{2}\right)+2 \pi\left(r_{2}^{2}-r_{1}^{2}\right)$

$\Rightarrow 2 \pi h\left(r_{1}+r_{2}\right)+2\left(\pi r_{2}^{2}-\pi r_{1}^{2}\right)$

Now putting the value of (b) in (a) we get

⟹ 2πh(r1 + r2) + 231 = 4620

⟹ 2π ∗ 7(r1 + r2) = 4389

⟹ π(r1 + r2) = 313.5 ... (c)

Now solving eq (b)

$\pi r_{1}^{2}-\pi r_{2}^{2}=115.5$

$\Rightarrow \pi r_{2}^{2}-\pi r_{1}^{2}=115.5$

$\Rightarrow \pi\left(r_{2}+r_{1}\right)\left(r_{2}-r_{1}\right) \ldots(d)$

Dividing equation (d) by (c) we get

$\frac{\left.\pi r_{1}+r_{2}\left(r_{2}-r_{1}\right)\right)}{\pi\left(r_{1}+r_{2}\right)}=\frac{115}{313.5}$

⟹ r2 − r1 = 0.3684 cm