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MAT126: Survey of Mathematical Methods (ABO1201F)

by Rosalyn
(Wadley, GA 30477)











































Discussion 2
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.
1. 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.
2. Record your dimensions and, using the appropriate formula, find the surface area of the room.
3. 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.
4. If a gallon of paint costs $22.95 plus 8% tax, what would be the total cost to paint the room?
5. One inch is equivalent to 2.54 centimeters. Convert your English measurements to metrics. Record each dimension in centimeters. Show your conversions.
6. Find the volume in cubic centimeters. Be neat and precise.
7. If each dimension (length, width, and height) is doubled, what happens to the volume of the room? Show your work.

Length: 15'8

Width: 13'8

Height: 8'14

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Jan 23, 2012
Survey of Mathematical Methods
by: Staff


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Part II

Total surface area of the room in square feet

(1 ft² = 144 in²)

= 108272 in² * 1 ft²/144 in²

= (108272 /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)

= (108272 /144) * ft² * (1)

= (108272 /144) * ft²

= 751.889 ft²

How many gallons would be required to paint the room?

Painting the room generally does not include the floor.

Gallons of paint = (Total surface area in ft²) * (1 gallon)/( ft² covered)

= (751.889 ft²) * (1 gallon/350 ft²)

= (751.889 /350) * (1 gallon) * (ft²/ft²)

= (751.889 /350) * (1 gallon) * (1)

= (751.889 /350) * (1 gallon)

= 2.14825 gallons

Rounding up (you must buy 3 gallons of paint, not 2.14825 gallons)

= 3 gallons


total cost to paint the room

Cost of Paint = (number of gallons)(cost per gallon) + (sales tax)

Cost of Paint = (3 gallons)*( $22.95/gallon) + (3 gallons)*( $22.95/gallon) (.08)

Cost of Paint = 3*$22.95*(gallons/gallons) + 3*$22.95*(gallons/gallons)*(.08)

Cost of Paint = 3*$22.95*(1) + 3*$22.95*(1)*(.08)

Cost of Paint = 3*$22.95 + 3*$22.95*(.08)

Cost of Paint = $68.85 + $68.85*(.08)

Cost of Paint = $68.85 + $5.51

Cost of Paint = $74.36



Convert your English measurements to metrics

Length: = (188 in)*(2.54 cm/in) = 477.52 cm

Width: = (164 in)*(2.54 cm/in) = 416.56 cm

Height: = (110 in)*(2.54 cm/in) = 279.4 cm


Find the volume in cubic centimeters.

Volume = length * width * height

= (477.52 cm) * (416.56 cm) * (279.4 cm)

= 55,577,055.2973 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



Jan 23, 2012
Survey of Mathematical Methods
by: Staff


Part I

Question:

by Rosalyn
(Wadley, GA 30477)


Discussion 2

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.

1. 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.

2. Record your dimensions and, using the appropriate formula, find the surface area of the room.

3. 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.

4. If a gallon of paint costs $22.95 plus 8% tax, what would be the total cost to paint the room?

5. One inch is equivalent to 2.54 centimeters. Convert your English measurements to metrics. Record each dimension in centimeters. Show your conversions.

6. Find the volume in cubic centimeters. Be neat and precise.

7. If each dimension (length, width, and height) is doubled, what happens to the volume of the room? Show your work.

Length: 15'8

Width: 13'8

Height: 8'14



Answer:


Measure the length, the width, and the height of a room.

Length: 15 ft 8 in

Width: 13 ft 8 in

Height: 8 ft 14 in


Convert the measurements to all inches

(1 ft = 12 inches)

Length:

15 ft 8 in

15 ft + 8 in

= 15 ft * 12 in/ft + 8 in

= 180 in + 8 in

= 188 in


Width: 13 ft 8 in

13 ft 8 in

13 ft + 8 in

= 13 ft * 12 in/ft + 8 in

= 156 in + 8 in

= 164 in


Height: 8 ft 14 in

8 ft + 14 in

= 8 ft * 12 in/ft + 14 in

= 96 in + 14 in

= 110 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 * (188 in) * (110 in) = 41360 in²

2nd two opposite walls = 2 * (164 in) * (110 in) = 36080 in²

Ceiling = (188 in) * (164 in) = 30832 in²



Total surface area of the room (excluding the floor)

= 41360 in² + 36080 in² + 30832 in²

= 108272 in²

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