Prism

Right angle prism, whose base is right triangle with leg a = 3 cm and hypotenuse c = 13 cm has same volume as a cube with an edge length of 3 dm.

a) Determine the height of the prism
b) Calculate the surface of the prism
c) What percentage of the cube's surface is prism surface area

Result

a) h =  1423 cm
b) S =  40806.3 cm2
c) p =  755.7 %

Solution:

x=132−32=12.65 cm S1=12.65⋅32=18.97 cm2 V=(10⋅3)3=27000=S1h h=2700018.97=1423  cm x = \sqrt{ 13^2- 3^2} = 12.65 \ cm \ \\ S_1 = \dfrac{ 12.65 \cdot 3 }{2} = 18.97 \ cm^2 \ \\ V = (10\cdot 3)^3 = 27000 = S_1 h \ \\ h = \dfrac{ 27000 } { 18.97 } = 1423 \ \text{ cm }
S=2S1+h(13+3+12.65)=40806.3 cm2S = 2 S_1 + h ( 13 + 3 + 12.65 ) = 40806.3 \ cm^2
Sk=6⋅(10⋅3)2=5400 cm2  p=100SSk=755.7%S_k = 6 \cdot (10 \cdot 3)^2 = 5400 \ cm^2 \ \\ \ \\ p = 100 \dfrac { S }{S_k} = 755.7 \%

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