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A monument in the shape of a square pyramid was built in a park.

The four lateral faces of the pyramid will be painted. The cost and coverage information for regular paint and metallic paint are shown in the table. Both paint types will be used on the monument.

PAINT TYPE COST(dollars per gallon) GALLONS(sq ft per gallon)
regular $35 200
metallic $100 80

The regular paint will require 2 coats, and the metallic paint will require 1 coat. Both paint types are sold only by the gallon. Based on the table, what is the least amount of money that should be budgeted to paint the monument?

A Monument In The Shape Of A Square Pyramid Was Built In A Park The Four Lateral Faces Of The Pyramid Will Be Painted The Cost And Coverage Information For Regu class=

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The least amount of money that should be budgeted to paint the monument is $1692.

Least amount of money that should be budgeted

First step

Using Pythagorean theorem to find the surface area

Since POR is a right triangle

Hence:

PO=20

BR=12

OR=12

PR=√20²+12²

PR=400+144

PR=544

Area of PBC=1/2×24×√544

Area of PBC=12√544

Lateral surface area=4×12√544

Lateral surface area=48√544

Lateral surface area=1119.54²ft

Second step

Since regular paint is  2 coats 200 sq. ft per gallon

Hence:

Number of gallons=1119.54×2/200

Number of gallons= 11.2 gallons

11.2×35= 392

1119.54/80=13 gallons

13×100 =1300

Last step

Least amount=392+1300

Least amount= $1692

Therefore the least amount of money that should be budgeted to paint the monument is $1692.

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