The height of prism

The base of a vertical prism is a right triangle with legs 30 cm and 40 cm long. The prism has the same volume as a cube with an edge length of 3 dm. Find the height of the prism in centimetres.

Final Answer:

h =  45 cm

Step-by-step explanation:

$$\begin{gathered} a=30\text{cm} \\ b=40\text{cm} \\ x=3\text{dm}\to \text{cm}=3\cdot 10\text{cm}=30\text{cm} \\ V=x^3=30^3=27000{\text{cm}}^3 \\ {S}_1=\frac{a\cdot b}{2}=\frac{30\cdot 40}{2}=600{\text{cm}}^2 \\ V=S_1\cdot h \\ h=V/S_1=27000/600=45\text{cm} \end{gathered}$$

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