A contractor is applying a specialized primer to a rectangular warehouse wall that is 60\t… — Armed Services Vocational Aptitude Battery (ASVAB)

A contractor is applying a specialized primer to a rectangular warehouse wall that is $60\text{ feet}$ long and $18\text{ feet}$ high. The wall contains a rectangular loading bay door measuring $30\text{ feet}$ long and $12\text{ feet}$ high, which will not receive the primer. If the primer material costs $\$15$ per square yard, what is the total cost, in dollars, of the primer needed for the wall?

Answer: 1200 $

Answer

1200

The total gross area of the wall is

60 \times 18 = 1080\text{ square feet}

. The area of the unpainted loading door is

30 \times 12 = 360\text{ square feet}

. Subtracting the door's area yields a net area of

720\text{ square feet}

to be primed. Because

1\text{ square yard}

equals

9\text{ square feet}

, the net area in square yards is

720 \div 9 = 80\text{ square yards}

. Finally, multiplying the

80\text{ square yards}

by the

\$15

cost per square yard gives a total cost of

\$1200

Step-by-Step Solution

Calculate the gross area of the warehouse wall.

1080\text{ sq ft}

Multiply the length (

60\text{ feet}

) by the height (

18\text{ feet}

) to find the total rectangular area before accounting for the door.

Calculate the area of the loading bay door.

360\text{ sq ft}

Multiply the door's length (

30\text{ feet}

) by its height (

12\text{ feet}

) to determine the area that will not be painted.

Find the net area to be primed.

720\text{ sq ft}

Subtract the area of the door from the gross wall area (

1080 - 360

) to find the exact surface area requiring primer.

Convert the net square footage into square yards.

80\text{ sq yd}

Since the cost is given per square yard, and there are

9\text{ square feet}

1\text{ square yard}

(

3\text{ ft} \times 3\text{ ft}

), divide the net area by 9 (

720 \div 9

Calculate the total cost of the primer.

\$1200

Multiply the required area in square yards (

80

) by the cost per square yard (

\$15

Key Concept

Calculating net rectangular area via subtractive cutouts and applying square unit conversions.

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Topics

More questions from this topic