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Surface Area and Volume of a Room

by Maria
(Rapid City, S.D.)











































room - length 8ft,width 8ft,height 8ft.

Do not use decimal numbers for the feet.

Convert the measurements to all inches for first step, and then convert back to square feet for next step.

Record dimensions with appropriate formula, find surface area of the room.

If gallon of paint covers about 350 square feet, how many gallons required to paint the room, rounded 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.

Converting English measurements to metrics, record each dimension in centimeters. Show conversions.

Find the volume in cubic centimeters.

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

Comments for Surface Area and Volume of a Room

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Feb 28, 2013
Calculating Area and Volume
by: Staff


Answer


Formulas for Surface Area and Volume - Rectangular Prism





Length, width, and height of room.


Length: 8 ft

Width: 8 ft

Height: 8 ft


Convert the measurements to all inches

(1 foot = 12 inches. )

Length:
8 ft
= 8 ft * 12 in/ft
= 96 in

Width: 10 ft exactly
8 ft
= 8 ft * 12 in/ft
= 96 in

Height: 9 ft 6 in
8 ft
= 8 ft * 12 in/ft
= 96 in


Compute the Surface Area of the Room in square inches

Surface area of 1 wall (all 6 surface areas are the same) = 96 in * 96 in

1 wall = 9216 in²

Calculations make no allowances for windows or doors.

1st two opposite walls = 2 * (9216 in²) = 18432 in²

2nd two opposite walls = 2 * (9216 in²) = 18432 in²

Ceiling = 9216 in²

Floor = 9216 in²


Total surface area of the room

Calculations do not include the floor.

= 18432 in² + 18432 in² + 9216 in²

= 46080 in²

Total surface area of the room (excluding the floor) in square feet

Convert Square Inches to Square Feet






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Feb 28, 2013
Calculating Area and Volume
by: Staff

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Part II

(notice that the units in²/in² cancel one another in the same way two numbers which are equal would cancel one another)


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)

Calculate Gallons of Paint Needed to Paint Room





total cost to paint the room

Cost of Paint = (number of gallons)(cost per gallon) + (sales tax)
Calculate the Cost of the Paint Needed to Paint Room





Cost of Paint = $24.79

Convert your English measurements to metrics

Length = Width = Height

Convert the English measurements to metrics






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Feb 28, 2013
Calculating Area and Volume
by: Staff

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Part III

Find the volume in cubic centimeters.

Volume = length * width * height

Volume in Cubic Centimeters







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

Volume Change when all Dimensions Double





If every dimension doubles, the new volume is 8 times the original volume.





Thanks for writing.

Staff
www.solving-math-problems.com



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