Vishy needs to paint the surfaces of three different spherical balls, having radii of 30 cm, 40 cm, and 50 cm, respectively. If the cost of paint needed to paint π $$cm^2$$​ is given as ₹0.60, what will be the total cost (in ₹) of the quantity of paint required to paint the surfaces of all the three balls mentioned above?

Correct option is B

Given:

Radius of three spheres =30cm, 40cm and 50cm

Cost of painting = ₹0.60 per $$\pi$$ $$cm^2$$​​

Formula Used:

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

Solution:

Surface area of sphere with radius 30cm  =$$4\times\pi \times (r^2)$$​​

​$$= 4\times \pi \times ((900)$$​​

​$$= 3600\pi cm^{2}$$​​

Surface area of sphere with radius 40cm  =$$4\times\pi \times (r^2)$$​​

​$$=4\times\pi \times (1600)$$​​

​$$= 6400\pi cm^{2}$$​​

Surface area of sphere with radius 50cm  =$$4\times\pi \times (r^2)$$​​

​$$=4\times\pi \times (2500)$$​​

​$$= 10000\pi cm^{2}$$​​

Total area to be painted = $$3600\pi + 6400\pi+10000\pi$$​​

​$$=20000\pi cm^2$$​​

Cost of painting =$$\frac{0.60}{\pi} \times 20000\pi cm^2$$​​

= ₹12000