# 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:

$x = \sqrt{ 13^2- 3^2} = 12.65 \ cm \ \\ S_1 = \dfrac{ 12.65 \cdot 3 }{2} = 18.97 \ cm^2 \ \\ V = (10\cdot 3)^3 = 27000 = S_1 h \ \\ h = \dfrac{ 27000 } { 18.97 } = 1423 \ \text{cm}$
$S = 2 S_1 + h ( 13 + 3 + 12.65 ) = 40806.3 \ \text{cm}^2$
$S_k = 6 \cdot (10 \cdot 3)^2 = 5400 \ cm^2 \ \\ \ \\ p = 100 \dfrac { S }{S_k} = 755.7 \%$

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