Calculating the surface area of a threedimensional object is similar to finding the area of a two dimensional object.


 Joel Wilson
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2 Calculating the surface area of a threedimensional object is similar to finding the area of a two dimensional object. Surface area is the sum of areas of all the faces or sides of a threedimensional object. Therefore, to calculate surface area of an object you must find the area of all sides and then add them together.
3 l w h A lw A (5)(3) l A 15cm w SA lw lh wh SA (5)(3) (5)(4) (3)(4) SA 94cm
4 Did You Know? A net is a two dimensional representation of a three dimensional object? Nets can be very helpful when calculating the surface area of a threedimensional object. Here is the net for the previous rectangular prism:
5 The circumference is an important measurement when determining the surface area of a cylinder as you will see in the next example. The circumference (perimeter) of a circle is C = πd where d is the diameter of the circle, or C = πr where r is the radius of the circle. Therefore, surface area of a cylinder can be calculated using the formula SA r dh Where d is the diameter of the cylinder SA r rh Where r is the radius of the cylinder
6 Find the surface area for the cylinder below: 10 cm 9 cm SA r rh SA (5) SA 439.8cm (5)(9) For radius = diameter / = 10 / = 5
7 Find the surface area for the triangular prism below: Step 1 Find the area of the triangular ends (there are of them!) h 5 cm 7 cm b 0 cm bh A [7][5] A A 17.5 A 35cm
8 Find the surface area for the triangular prism below: 5 cm 7 cm w 0 cm l Step Determine the area of the rectangular bottom A lw A (0)(7) A 140cm
9 Find the surface area for the triangular prism below: Step 3 Determine the area of the rectangular sides (there are two of them!) 6.1 cm 5 cm 7 cm 5 cm b c 3.5 cm a 6.1 cm 0 cm We only know the length (0 cm) We must solve for the width using Pythagorean Theorem c c c a b ( 3.5) (5) c 37.5 c 37.5 c 6. 1cm Therefore, for the Area: A ( lw) A (0)(6.1) A 1 A 44cm
10 Find the surface area for the triangular prism below: Step 4 Add up all the Areas 6.1 cm 5 cm 7 cm 0 cm Total Surface Area = A TRIANGLE SIDES + A RECTANGULAR BOTTOM + A RECTANGULAR SIDE = = 419 cm Therefore, total surface area of the prism is 419 square centimetres. Now that you have had the opportunity to calculate the surface area of prisms, you will apply this knowledge to solve some realworld applications. END OF DAY 1
11 Joel s bedroom is 1 feet by 15 feet and the height from the floor to the ceiling is 10ft. He decides he is going to paint his bedroom walls dark green and the ceiling white. To ensure full coverage, the entire room will require two coats of paint. If a 1 gallon can of paint covers approximately 400 square feet, how many cans of each colour of paint, green and white, does Joel need to purchase? SOLUTION 10 feet We need to find the area of each given side (the 4 walls and the roof) and then find out the amount of paint for each colour 15 feet 1 feet
12 10 feet 15 feet 1 feet Step 1 Find area of front walls (there are two of them!) Step Find area of side walls (there are two of them!) Area = (lw) = [(1)(10)] = (10) = 40 ft Area = (lw) = [(15)(10)] = (150) = 300 ft Total wall area = = 540 ft
13 Step 3 Find the number of cans of paint to cover the walls 10 feet 15 feet Given that the total wall area is 540 ft and that two coats of paint are needed... Total area to be covered is 540 = 1080 ft. 1 feet # of cans = total area / area covered by one gallon can = 1080 ft / 400 ft =.7 gallon cans Therefore 3 gallon cans of green paint should be used to cover the walls
14 Step 4 Find the area of the roof 1 feet 10 feet 15 feet A = lw = (15)(1) = 180 ft Step 5 Determine the # of gallon cans required Since two coats are required 180 = 360 ft # of cans = total area / area covered by one gallon can = 360 ft / 400 ft = 0.9 gallon cans Therefore, only one can of white paint is required to paint the roof
15 Christmas time is approaching and you have purchased the same gift for each of your 14 coworkers. The gifts are packaged in boxes with dimensions by 1 5 by If there are 80 square feet of wrapping paper per roll, how many rolls of wrapping paper do you require to wrap all your gifts? / 1 = 0.17 ft. Total = =.17 ft / 1 = 0.9 ft. Total = = 1.9 ft 5 / 1 = 0.4 ft. Total = = 1.4 ft Step 1 Since we want the surface area in square feet (ft ), we need to change all measurements to feet Divide the inches ( ) measurement by 1 and add it to the feet measurement ( )
16 Christmas time is approaching and you have purchased the same gift for each of your 14 coworkers. The gifts are packaged in boxes with dimensions by 1 5 by If there are 80 square feet of wrapping paper per roll, how many rolls of wrapping paper do you require to wrap all your gifts?.17 ft l 1.9 ft h 1.4 ft w Step Calculate the surface area of one gift A = lw + lh + wh = (.17)(1.4) + (.17)(1.9) + (1.4)(1.9) = = ft (or square feet) Since there area 14 people = ft
17 Christmas time is approaching and you have purchased the same gift for each of your 14 coworkers. The gifts are packaged in boxes with dimensions by 1 5 by If there are 80 square feet of wrapping paper per roll, how many rolls of wrapping paper do you require to wrap all your gifts?.17 ft 1.9 ft 1.4 ft Step 3 Determine how many rolls are required to wrap gifts for 14 people Since one roll covers 80 ft... # of rolls = Total surface area / area per roll = ft / 80 ft = 3.5 rolls Therefore 4 rolls should be purchased to cover the presents
18 ASSIGNMENT 1. Determine the surface area of the following prisms: (a) (b). You have been asked to paint a room that is 15 long, 11 wide. The paint can indicates that 1 gallon of paint will cover 50m. How many cans must be purchased if you must apply two coats of paint and the walls are 10 high? (Note: The ceiling and floor will not be painted) Include a net with your solution.
19 Homework pg (Day 1) #1 to 6 (Day ) 7 to 9, 11
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