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Grade -10 (SEE) Math Combined Solid, Mensuration

If the pillars with pyramid are painted at the rate of Rs 75 find total cost.

Two pillars of height 8 feet each with four faces shown of the gate of a stadium have one-one pyramid of height 4 feet each having same base on their tops. The base of each pillar is 6 ft x 6 ft. If the pillars with pyramid are painted at the rate of Rs. 75 per square feet, what will be the total cost?

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Tribhuvan University > Institute of Science and Technology > B.Sc. (CSIT)

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 = 2lh1 
= 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

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