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 π = $$\frac{22}7$$​)

Correct option is B

Given:

The diameter of the spherical vessel = 14 cm

The cost of painting the entire spherical vessel = ₹21,560

We need to find the cost of painting per square centimetre.

Use $$\pi = \frac{22}{7}.$$​​

Formula Used:

Surface area of the sphere(A) = $$4 \pi r^2$$​​

where r is the radius of the sphere.

​$$\text{Cost per cm}^2 = \frac{\text{Total cost}}{\text{Surface area}}$$​

Solution:

Since the diameter is 14 cm, the radius r is:

​$$r = \frac{\text{Diameter}}{2} = \frac{14}{2} = 7 \, \text{cm}$$​​

Using the formula for the surface area of a sphere:

A = $$4 \pi r^2 = 4 \times \frac{22}{7} \times (7)^2$$​

A = $$4 \times \frac{22}{7} \times 49 = 4 \times \frac{1078}{7} = \frac{4312}{7} = 616 \, \text{cm}^2$$​

The total cost of painting is ₹21,560, so the cost per square centimetre is:

​$$\text{Cost per cm}^2 = \frac{21,560}{616} = 35 \, \text{₹/cm}^2$$​​

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