Question

If a rod of 2 cm diameter and 30 cm length is connected with a wire of 3m length and diameter 1 cm. Then find the total surface area.
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Answer 1

Total surface area of whole system $S = 182\pi$ $cm^{2}$

Explanation:

Diameter of rod $D_r = \textrm{2 cm}$⇒ $R = \textrm{1 cm}$

Length of rod $L = \textrm{30 cm}$

Diameter of wire $r = \textrm{1 cm}$ ⇒ $r = \textrm{0.5 cm}$

Length of wire $l = \textrm{3 m}$ ⇒ $= \textrm{300 cm}$

The some diametric surface area of rod is hide by the diametric surface area of wire,

So the net surface area of rod $S_r = \pi R L + 2\pi R^{2} - \pi r^{2}$  

⇒ $S_r = 30\times 1 \pi + 2\pi1^{2} - \pi (0.5)^{2}$

⇒ $S_r =\frac{127\pi}{4}$

One of the side area is in connection so the only one side area will be considered

So the net surface area of wire $S_w = \pi rl + \pi r^{2}$

⇒ $S_w = 300 \times 0.5 \pi + \pi (0.5)^{2}$

⇒ $S_w = 150 \pi + \frac{\pi}{4}$

⇒ $S_w = \frac{601 \pi}{4}$

Total surface area of whole system $S = S_r +S_w$

⇒ $S = \frac{127\pi}{4} +\frac{601 \pi}{4}$

⇒ $S = \frac{728\pi}{4}$$cm^{2}$

Total surface area of whole system $S = 182\pi$ $cm^{2}$