A right-angled prism, whose base is a right triangle with leg a = 3 cm and hypotenuse c = 6 cm, has the same volume as a cube with an edge length of 1 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 answer:

h =  128.3 cm
S =  1837 cm2
x =  306.2 %

Step-by-step explanation:

a=3 cm c=6 cm k=1 dm cm=1 10  cm=10 cm  c2=a2+b2 b=c2a2=6232=3 3 cm5.1962 cm S1=2a b=23 5.19627.7942 cm2 V=k3=103=1000 cm3  V = S1   h h=V/S1=1000/7.7942=128.3 cm
o=a+b+c=3+5.1962+614.1962 cm S=2 S1+o h=2 7.7942+14.1962 128.3001=1837 cm2
S2=6 k2=6 102=600 cm2  x=100 S2S=100 6001836.9557=306.2%

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