Question

The internal and external diameters of a hollow hemispherical vessel 14 cm and 21 cm respectively. The cost of silver plating is ₹0.40 per $c{m}^2$. Find the total cost of silver plating the vessel all over.

• A. ₹475
• B. ₹470
• C. ₹477.40
• D. ₹577.40

Answer 1

The correct option is C ₹477.40

Let inner and outer radius of hollow hemispherical vessel be r and R respectively.
$r=\frac{14}{2}cm,R=\frac{21}{2}cm$
Total surface area of hemispherical vessel
= Outer curved surface area + Inner curved surface area + Area of ring
$=2\pi R^2+2\pi r^2+(\pi R^2-\pi r^2)$
$=3\pi R^2+\pi r^2$
$=\pi (3R^2+r^2)=\frac{22}{7}(3\times {\left(\frac{21}{2}\right)}^2+{\left(\frac{14}{2}\right)}^2)$
$=\frac{22}{7}(\frac{1323}{4}+\frac{196}{4})$
$=\frac{22}{7}\times \frac{1519}{4}=\frac{2387}{2}c{m}^2$
Thus, total cost of silver plating
$=0.40\times \frac{2387}{2}=477.40$

So, option c is correct.