Find the surface area of the water in the given prism

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SUMMARY

The discussion focuses on calculating the surface area of water in a prism, specifically addressing part c(ii) of a mathematical problem. The user calculates three areas: A1, A2, and A3, resulting in a total surface area of 2.494 m². The calculations involve using the formula for the area of a trapezoid and the area of a rectangle, along with principles of similarity in triangles to derive necessary dimensions. The user clarifies the importance of significant figures in their final answer, emphasizing that 0.8386 rounds to 0.839 when expressed to three significant figures.

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  • Understanding of geometric formulas for area calculation
  • Familiarity with significant figures and rounding rules
  • Knowledge of similarity in triangles
  • Basic proficiency in mathematical problem-solving
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  • Study the properties of trapezoids and their area formulas
  • Learn about significant figures and their application in calculations
  • Explore the concept of similarity in geometric figures
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Students in geometry, mathematics educators, and anyone involved in solving surface area problems in three-dimensional shapes.

chwala
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Homework Statement
See attached ( past paper question)
Relevant Equations
Knowledge of prisms
My query in only on the highlighted part...c.ii.

Find the question below;
1645356762096.png

1645356817111.png

1645356847660.png

Find the markscheme here

1645356956426.png

1645357012052.png
part c(ii) does not seem correct as i have;
##A_1=0.5 ×(0.65+0.84)0.3 ×2=0.447m^2##
##A_2 = 0.65 ×1.6=1.04m^2##
##A_3 = (0.3146 × 1.6)2=1.00672m^2##
Total surface area = ##A_1+A_2+A_3=0.447+1.04+1.00672=2.494m^2##...

For part c.(i), i was able to use similarity (i used a right angle triangle from the cross-section) to show that,
i.e ##\dfrac {0.477}{0.15}##=##\dfrac {0.3}{x}##
##x=0.094## therefore, ##w = 0.65+2(0.094)=0.8386≈0.84## to 3 2 significant figures.
 
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aaargh! its the english man, i figured it out, ##0.84 × 1.6! ## Area of surface and not Surface area! phew:cool:
 
chwala said:
##x=0.094## therefore, ##w = 0.65+2(0.094)=0.8386≈0.84## to 3 significant figures.
0.8386 to 3 significant figures amounts to 0.839 :smile:

(i.e. a leading zero does not count as a significant figure)

##\ ##
 
BvU said:
0.8386 to 3 significant figures amounts to 0.839 :smile:

(i.e. a leading zero does not count as a significant figure)

##\ ##
:)):biggrin:...to two significant figures...yeah, i know that. cheers bvu...
 

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