Solution:

Given:-

In pillars formed by prism and pyramid,

Length of the square base (l) = 6 feet

Height of prism = 8 feet

Height of pyramid = 4 feet

No of pillars = 2

Rate of painting = Rs. 75/sq.ft

To find: Total cost of painting on two pillars.

Here,

Slant height of the square based pyramid (h1)

= \(\sqrt{h^2+\left(\frac{l}{2}\right)^2}\)

= \(\sqrt{4^2+\left(\frac{6}{2}\right)^2}\)

= 5 feet

And, Perimeter of the square base = 4l = 4 x 6 feet = 24 feet

By formula, L.S.A of a square based prism

= Perimeter of base x height

= 24 feet x 8 feet

= 192 sq. ft

Again, by formula

LSA of a square based pyramid = 2lh_{1}

= 2 x 6 ft x 5 ft

= 60 sq ft

Here, Surface area of each pillar

= LSA of prism + LSA of pyramid

= 192 sq ft + 60 sq ft

= 252 sq ft

∴ Surface area of two pillars = 2 x 252 sq ft = 504 sq ft

Now, total cost of painting = Cost per sq ft x total area = Rs 75 x 504 = Rs. 37,800

∴ The total cost of painting two pillars = Rs. 37,800