Question

A cylindrical vessel open at the top has diameter 20 cm and height 14 cm. Find the cost of tin-plating it on the inside at the rate of 50 paise per hundred square centimetre.

 

Answer 1

\[\text{ Given } : \]

\[\text{Diameter, d = 20 cm} \]

\[\text{ Radius, r = 10 cm } \]

\[\text{ Height, h = 14 cm} \]

\[\text{ Area inside the cylindrical vessel that is to be tin - plated } = S\]

\[S = 2\pi rh + \pi r^2 \]

\[ = 2\pi \times 10 \times 14 + \pi \times {10}^2 \]

\[ = 280\pi + 100\pi\]

\[ = 380 \times \frac{22}{7} {cm}^2 \]

\[ = \frac{8360}{7} {cm}^2 \]

\[\text{ According to question: }  \]

\[\text{ Cost per 100 {cm } }^2 = 50 \text{ paise }  \]

\[\text{ Cost per {cm} } ^2 = Rs 0 . 005\]

\[\text{ Cost of tin - plating the area inside the cylindrical vessel } = Rs 0 . 005 \times \frac{8360}{7}\]

\[ = Rs \frac{41 . 8}{7} = Rs 5 . 97\]

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