Question

The gate of a stadium ha two pillars each of height 10ft.with four visible lateral faces and 3ft*3ft bases .the top of eaxh pillar has combined pyaramid of height2ft.If the combined structures of both pillars and pyramid are painted at the rate of rs 80 persq.ft.calcuate the total cost of painting.
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Answer 1

The pillars and the pyramids in the stadium gate means that we have to calculate the area of the items that make up the gate one after the other. At the end of the calculation, the calculated areas are then added up.

The total cost of painting is Rs.21344

First, we calculate the area of 1 side of 1 pillar using:

$A = Height * Base$

Where

$Height = 10ft$ --- Height of the pillar

$Base = 3ft$ --- Base of the pillar

So:

$A = 10ft * 3ft$

$A = 30ft^2$

The area of the 4 sides of the pillar is:

$A_2 = 4 * A$ --- i.e. 4 multiplied by the area of 1 side

$A_2 = 4 * 30ft^2$

$A_2 = 120ft^2$

The area of the 2 pillars is:

$Area_1 = 2 * A_2$ --- i.e. 2 multiplied by the area of 1

$Area_1 = 2 * 120ft^2$

$Area_1 = 240ft^2$

Because one part of the pyramid won't be visible, we calculate the area of the pyramid using:

$Area = lw + l\sqrt{(w/2)^2 + h^2} + w\sqrt{(l/2)^2 + h^2}$

Where:

$h = 2$ -- the height

$l = w = 3$ --- the base of the pillar is the length & width of the pyramid.

So, we have:

$Area = 3\sqrt{(2/2)^2 + 2^2} + 3\sqrt{(2/2)^2 + 2^2}$

$Area = 3\sqrt{1 + 4} + 3\sqrt{1 + 4}$

$Area = 3\sqrt{5} + 3\sqrt{5}$

$Area = 6\sqrt{5}$

For the two pyramids, the area is:

$Area_2 = 2 * 6\sqrt 5$ -- 2 multiplied by area of 1

$Area_2 = 12\sqrt 5$

$Area_2 = 26.8$

So, the total area to be painted is:

$Total = Area_1 + Area_2$ --- the sum of the area of the pillars and the pyramids

$Total = 240+26.8$

$Total = 266.8ft^2$

The unit cost of paint is:

Rate = Rs80 per sq.ft

The total cost of painting is:

$Cost = 80 * 266.8$

$Cost = Rs.21344$

Hence, the total cost of painting is Rs.21344.

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