The cost of painting a spherical vessel of diameter 14 cm is ₹21,560. What is the cost of painting (in ₹) per square centimetre? (Use $\pi =\frac{22}{7}$ )

The correct option is 35.

Given:
Total cost of painting the spherical vessel = ₹21,560
Diameter of the spherical vessel (d) = 14 cm

First, find the radius (r) of the spherical vessel:

$r=\frac{d}{2}=\frac{14}{2}=7\text{cm}$

Next, calculate the total surface area of the spherical vessel using the formula for the surface area of a sphere:

$\text{Surface Area}=4\pi r^2$

Substitute $\pi =\frac{22}{7}$ and $r=7\text{cm}$ into the formula:

$\text{Surface Area}=4\times \frac{22}{7}\times 7^2$

$\text{Surface Area}=4\times \frac{22}{7}\times 49$

$\text{Surface Area}=4\times 22\times 7=616{\text{cm}}^2$

Now, compute the cost of painting per square centimetre:

$\text{Cost per sq cm}=\frac{\text{Total Cost}}{\text{Total Surface Area}}$

$\text{Cost per sq cm}=\frac{21560}{616}=35$

Thus, the cost of painting per square centimetre is ₹35.