Questions: You've been tasked with adding soundproofing panels to 10 private offices. Each office is 12 feet by 16 feet with 8 -foot ceilings. Paneling sheets are 4 feet by 8 feet, and are only applied to the walls, not the ceiling. Assume that each office has 4 walls. How many panels are required for all the offices? A. 14 B. 140 C. 70 D. 448

Solution Steps

To determine the number of soundproofing panels needed, calculate the total wall area for one office and then for all offices. Divide the total wall area by the area of one panel to find the number of panels required.

1. Calculate the perimeter of one office to find the total wall length.
2. Multiply the perimeter by the ceiling height to get the total wall area for one office.
3. Multiply the wall area of one office by the number of offices.
4. Divide the total wall area by the area of one panel to find the number of panels needed.

The perimeter of one office is calculated using the formula: \[ \text{Perimeter} = 2 \times (\text{length} + \text{width}) = 2 \times (12 + 16) = 56 \text{ feet} \]

The total wall area for one office is given by: \[ \text{Wall Area} = \text{Perimeter} \times \text{height} = 56 \times 8 = 448 \text{ square feet} \]

Multiply the wall area of one office by the number of offices: \[ \text{Total Wall Area} = 448 \times 10 = 4480 \text{ square feet} \]

The area of one panel is: \[ \text{Panel Area} = \text{panel length} \times \text{panel width} = 4 \times 8 = 32 \text{ square feet} \]

Divide the total wall area by the area of one panel to find the number of panels needed: \[ \text{Number of Panels} = \frac{4480}{32} = 140 \]

Final Answer