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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

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Apr 14, 2011
Measurements
by: Staff


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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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