The internal and external diameters of a hollow hemispherical vessel are 14 cm and 21 cm respectively. The cost of silver plating of 1 cm² of its surface is ₹ 32. Find the total cost of silver plating the vessel all over.

Given,

External radius (R) = $\dfrac{21}{2}$ = 10.5 cm

Internal radius (r) = $\dfrac{14}{2}$ = 7 cm

By formula,

Total surface area of hollow hemisphere (T)

= Curved surface area of inner hemispherical surface + Curved surface area of outer hemispherical surface + Area of shaded annular disc.

= 2πr² + 2πR² + πR² - πr²

= 3πR² + πr²

Substituting values we get :

$T = 3 \times \dfrac{22}{7} \times (10.5)^2 - \dfrac{22}{7} \times 7^2 \\[1em] = \dfrac{66}{7} \times 110.25 + 154 \\[1em] = 66 \times 15.75 + 154 \\[1em] = 1039.5 + 154 \\[1em] = 1193.5 \text{ cm}^2$

Given,

Cost of silver plating of 1 cm² of its surface is ₹ 32.

Total cost = 1193.5 × ₹ 32 = ₹ 38192

Hence, cost of silver plating the vessel = ₹ 38192.