Question

A cylindrical vessel, without lid, has to be tin-coated on its both sides. If the radius of the base is 70 cm and its height is 1.4 m, calculate the cost of tin-coating at the rate of Rs 3.50 per 1000 cm².

 

Answer 1

\[\text{ Let r cm and h cm be the radius of the cylindrical vessel } . \]
\[\text{ Given: } \]
\[\text{ Radius, r = 70 cm} \]
\[ \text{ Height, h = 1 . 4 m = 140 cm } \]
\[\text{ Rate of tin - plating = Rs 3 . 50 per 1000 square centimetre } \]
\[\text{ Cost of tin - plating the cylindrical vessel on both the surfaces (inner and outer): } \]
\[\text{ Total suface area of a vessel = Area of the inner and the outer side of the base + Area of the inner and the outer curved surface } \]
\[ = 2\left( \pi r^2 + 2\pi rh \right)\]
\[ = 2\pi r\left( r + 2h \right)\]
\[ = 2 \times \frac{22}{7} \times 70 \times \left( 70 + 2 \times 140 \right)\]
\[ = 44 \times 10 \times 350\]
\[ = 154000 {\text{ cm } }^2 \]
\[\text{ Cost of painting at the rate of Rs 3 . 50 per 1000 {cm} }^2 = 154000 \times \frac{3 . 50}{1000} = Rs 539\]
\[\text{ Therefore, cost of painting is Rs 539 }  . \]