Prism

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

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

Correct result:

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

Solution:

x=13232=12.65 cm S1=12.6532=18.97 cm2 V=(103)3=27000=S1h h=2700018.97=1423 cm
S=2S1+h(13+3+12.65)=40806.3 cm2
Sk=6(103)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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