Question

how many cubic feet of air are heated in a room 286 long, 220 wide, and 86 high? round the answer to 2 significant digits. 5300 cu ft 5900 cu ft 5329.5 cu ft 5200 ft

Explanation:

Step1: Convert inches to feet

• For length: \(28'6'' = 28 + \frac{6}{12}=28.5\) feet (since 1 foot = 12 inches, so 6 inches is \(\frac{6}{12}\) feet)
• For width: \(22'0'' = 22\) feet (no inches, so it's just 22 feet)
• For height: \(8'6'' = 8+\frac{6}{12} = 8.5\) feet

Step2: Calculate volume of the room

The volume \(V\) of a rectangular room (which is a rectangular prism) is given by the formula \(V=\text{length}\times\text{width}\times\text{height}\)

Substitute the values: \(V = 28.5\times22\times8.5\)

First, calculate \(28.5\times22 = 627\)

Then, calculate \(627\times8.5=5329.5\) cubic feet

Step3: Round to 2 significant digits

To round \(5329.5\) to 2 significant digits, we look at the first two non - zero digits. The first two significant digits are 5 and 3. The next digit is 2, which is less than 5, but wait, actually, when rounding to 2 significant digits, we consider the number in scientific notation. \(5329.5=5.3295\times 10^{3}\). Rounding \(5.3295\) to 2 significant digits gives \(5.3\times 10^{3}=5300\) (since the third digit 2 is less than 5, we keep the second digit as it is)

Answer:

5300 cu ft (assuming one of the options with 5300 cu ft is the correct one, probably the first or second option with 5300 cu ft as the value)