Examkin

Soru

Zorluk: ZorRectangular Area Applications

A hotel manager is ordering custom acoustic paneling for a large rectangular conference room wall. The wall measures 36 feet36 \text{ feet} in length and 15 feet15 \text{ feet} in height. The wall contains 33 identical rectangular windows, each measuring 6 feet6 \text{ feet} wide and 4 feet4 \text{ feet} high, which will not be covered by the paneling. If the acoustic paneling costs $45\$45 per square yard, what is the total cost of the paneling needed for this wall?

  1. A
    $1,530\$1,530
  2. $2,340\$2,340Cevap
  3. C
    $7,020\$7,020
  4. D
    $21,060\$21,060

Cevap

The total cost of the acoustic paneling needed is $2,340\$2,340.
The correct answer is found by first determining the gross area of the wall (36×15=540 sq ft36 \times 15 = 540 \text{ sq ft}) and subtracting the area of the three windows (3×24=72 sq ft3 \times 24 = 72 \text{ sq ft}) to get a net coverage area of 468 sq ft468 \text{ sq ft}. Because the paneling is sold by the square yard, the square footage must be converted by dividing by 99 (since 1 sq yd=9 sq ft1 \text{ sq yd} = 9 \text{ sq ft}). This gives 52 sq yd52 \text{ sq yd}. Multiplying this by the price of $45\$45 per square yard yields a total cost of $2,340\$2,340.

Adım Adım Çözüm

1
Calculate the total area of the rectangular wall in square feet.
36×15=540 sq ft36 \times 15 = 540 \text{ sq ft}
The gross area is needed before accounting for the cutouts.
2
Calculate the combined area of the three identical windows.
3×(6×4)=72 sq ft3 \times (6 \times 4) = 72 \text{ sq ft}
The windows will not be covered by paneling, so their total area must be subtracted.
3
Subtract the window area from the total wall area to find the net area to be covered.
540−72=468 sq ft540 - 72 = 468 \text{ sq ft}
This provides the exact amount of paneling needed in square feet.
4
Convert the net area from square feet to square yards.
468÷9=52 sq yd468 \div 9 = 52 \text{ sq yd}
Since the cost is given per square yard, the area must match this unit. There are 3×3=9 sq ft3 \times 3 = 9 \text{ sq ft} in a square yard.
5
Multiply the required area in square yards by the cost per square yard.
52×45=$2,34052 \times 45 = \$2,340
This yields the total cost for the materials.

Anahtar Kavram

Calculating subtractive rectangular area and converting square units before applying a cost rate.
Bu soruyu puanla

Konular

Rectangular Area Applications

Bu konudan daha fazla soru