  # Measurements

This Discussion tests your ability to use a ruler and convert from Standard English measure to Metrics. You will then apply your knowledge of the geometric measurements of area and volume through real world problems.
Choose a room in your house. Measure the length, the width, and the height. Make sure you use feet and inches. Most rooms are not a whole number, such as 10 feet; they are 10 feet and 3 inches, or 9 feet 6 inches, etc.
NOTE: Do not use decimal numbers for the feet. For example, do not write 10.3 to mean 10’3”, because that is incorrect. Convert the measurements to all inches for step 2, and then convert back to square feet for step 3.
Record your dimensions and, using the appropriate formula, find the surface area of the room.
A gallon of paint covers about 350 square feet. How many gallons would be required to paint the room? Round up to the nearest gallon.
If a gallon of paint costs \$22.95 plus 8% tax, what would be the total cost to paint the room?
One inch is equivalent to 2.54 centimeters. Convert your English measurements to metrics. Record each dimension in centimeters. Show your conversions.
Find the volume in cubic centimeters. Be neat and precise.
If each dimension (length, width, and height) is doubled, what happens to the volume of the room? Show your work.
Respond to at least two of your classmates’ postings. Review their calculations and determine if their results seem reasonable for the size of the room.

### Comments for Measurements

 Apr 14, 2011 Measurements by: Staff ------------------------------------------------------------------- Part II Total surface area of the room in square feet = 62046 in² * 1 ft²/144 in² = (62046/144) * ft² * (in²/ in²) (notice that the units in²/in² cancel one another in the same way two numbers which are equal would cancel one another) = (62046/144) * ft² * (1) = (62046/144) * ft² = 62046/144 * ft² = 430.875 ft² How many gallons would be required to paint the room? Gallons of paint = (Total surface area in ft²) * (1 gallon)/( ft² covered) = (430.875 ft²) * (1 gallon/350 ft²) = (430.875/350) * (1 gallon) * (ft²/ft²) = (430.875/350) * (1 gallon) * (1) = (430.875/350) * (1 gallon) = 1.23107 gallons Rounding up = 2 gallons total cost to paint the room Cost of Paint = (number of gallons)(cost per gallon) + (sales tax) Cost of Paint = (2 gallons)*( \$22.95/gallon) + (2 gallons)*( \$22.95/gallon) (.08) Cost of Paint = 2*\$22.95*(gallons/gallons) + 2*\$22.95*(gallons/gallons)*(.08) Cost of Paint = 2*\$22.95*(1) + 2*\$22.95*(1)*(.08) Cost of Paint = 2*\$22.95 + 2*\$22.95*(.08) Cost of Paint = \$45.90 + \$45.90*(.08) Cost of Paint = \$45.90 + \$3.67 Cost of Paint = \$49.57 Convert your English measurements to metrics Length: = (123 in)*(2.54 cm/in) = 312.42 cm Width: = (122 in)*(2.54 cm/in) = 309.88 cm Height: = (96 in)*(2.54 cm/in) = 243.84 cm Find the volume in cubic centimeters. Volume = length * width * height = (312.42 cm) * (309.88 cm) * (243.84 cm) = 23,606,800 cm³ If each dimension (length, width, and height) is doubled, what happens to the volume of the room? Volume1 = length * width * height Volume2 = 2*length * 2*width * 2*height Divide Volume2 by Volume1 Volume2/Volume1 = (2*length * 2*width * 2*height)/(length * width * height) Volume2/Volume1 = (2*length/length) * (2*width/width) * (2*height/height) Volume2/Volume1 = (2*1) * (2*1) * (2*1) Volume2/Volume1 = 2 * 2 * 2 Volume2/Volume1 = 8 If every dimension doubles, the new volume is 8 times the original volume. Thanks for writing. Staff www.solving-math-problems.com

 Apr 14, 2011 Measurements by: Staff Part I The question: This Discussion tests your ability to use a ruler and convert from Standard English measure to Metrics. You will then apply your knowledge of the geometric measurements of area and volume through real world problems. Choose a room in your house. Measure the length, the width, and the height. Make sure you use feet and inches. Most rooms are not a whole number, such as 10 feet; they are 10 feet and 3 inches, or 9 feet 6 inches, etc. NOTE: Do not use decimal numbers for the feet. For example, do not write 10.3 to mean 10’3”, because that is incorrect. Convert the measurements to all inches for step 2, and then convert back to square feet for step 3. Record your dimensions and, using the appropriate formula, find the surface area of the room. A gallon of paint covers about 350 square feet. How many gallons would be required to paint the room? Round up to the nearest gallon. If a gallon of paint costs \$22.95 plus 8% tax, what would be the total cost to paint the room? One inch is equivalent to 2.54 centimeters. Convert your English measurements to metrics. Record each dimension in centimeters. Show your conversions. Find the volume in cubic centimeters. Be neat and precise. If each dimension (length, width, and height) is doubled, what happens to the volume of the room? Show your work. Respond to at least two of your classmates’ postings. Review their calculations and determine if their results seem reasonable for the size of the room. The answer: Measure the length, the width, and the height of a room. Length: 10 ft 3 in Width: 10 ft 2 in Height: 8 ft 0 in Convert the measurements to all inches (10 ft = 10 ft * 12 in/ft = 120 inches) Length: 120 in + 3 in = 123 in Width: 120 in + 2 in = 122 in Height: 8 ft * 12 in/ft = 96 in Compute the Surface Area of the Room in square feet Surface area of 1 wall = width * height Calculations make no allowances for windows or doors. Calculations do not include the floor. 1st two opposite walls = 2 * (123 in) * (96 in) = 23616 in² 2nd two opposite walls = 2 * (122 in) * (96 in) = 23424 in² Ceiling = (123 in) * (122 in) = 15006 in² Total surface area of the room = 23616 in² + 23424 in² + 15006 in² = 62046 in² -------------------------------------------------------------------

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