Answer:
1. 36 [tex]m^{2}[/tex]
2. 333.125 [tex]ft^{3}[/tex]
3. 210 [tex]ft^{3}[/tex]
4. Yes, Martina's estimate is reasonable.
Step-by-step explanation:
Numbering the rectangular surfaces, we have:
Area of a rectangle = length x width
For surface 1: Area = 2 x 2.4
= 4.8 [tex]m^{2}[/tex]
For surface 2: Area = 3 x 2.4
= 7.2 [tex]m^{2}[/tex]
For surface 3: Area = 3 x 2
= 6.0 [tex]m^{2}[/tex]
For surface 4: Area = 3 x 2.4
= 7.2 [tex]m^{2}[/tex]
For surface 5: Area = 2 x 2.4
= 4.8 [tex]m^{2}[/tex]
For surface 6: Area = 3 x 2
= 6.0 [tex]m^{2}[/tex]
Total surface area of the rectangular prism = (2 x 4.8) + (2 x 7.2) + (2 x 6.0)
= 36 [tex]m^{2}[/tex]
2. length = 10.25 ft
width = 5 ft
height = 6.5 ft
Thus,
volume = l x w x h
= 10.25 x 5 x 6.5
= 333.125 [tex]ft^{3}[/tex]
3. length = 15 ft
width = 7 ft
height = 2 ft
So that,
volume = l x w x h
= 15 x 7 x 2
= 210 [tex]ft^{3}[/tex]
4. For a rectangular prism, area of the opposite surfaces are equal. So that;
Area of rectangle = length x width
For surface 1: Area = 13.0 x 6
= 78.0 [tex]ft^{2}[/tex]
For surface 2: Area = 13.0 x 8
= 104.0 [tex]ft^{2}[/tex]
For surface 3: Area = 6 x 8
= 48 [tex]ft^{2}[/tex]
Surface area of the prism = (2 x 78.0) + (2 x 104.0) + (2 x 48)
= 460.0 [tex]ft^{2}[/tex]
Therefore, Martina's estimate is reasonable.
