Prism volume

Calculate the volume and surface area of the body that is created by cutting out a three-sided prism of the same height from a cuboid with dimensions of 10 cm, 15 cm, and 20 cm, whose base is a right-angled triangle with dimensions of 3 cm, 4 cm, and 5 cm.

Final Answer:

V =  2880 cm³
S =  1248 cm²

Step-by-step explanation:

$$\begin{gathered} a=10\text{cm} \\ b=15\text{cm} \\ c=20\text{cm} \\ {a}_1=3\text{cm} \\ {a}_2=4\text{cm} \\ {a}_3=5\text{cm} \\ {S}_1=a_1\cdot a_2/2=3\cdot 4/2=6{\text{cm}}^2 \\ {S}_2=a\cdot b=10\cdot 15=150{\text{cm}}^2 \\ {S}_3=S_2-S_1=150-6=144{\text{cm}}^2 \\ V=S_3\cdot c=144\cdot 20=2880{\text{cm}}^3 \end{gathered}$$

$$\begin{gathered} o=a+b+(a-a_1)+a_3+(b-a_2)=10+15+(10-3)+5+(15-4)=48\text{cm} \\ S=2\cdot S_3+o\cdot c=2\cdot 144+48\cdot 20=1248{\text{cm}}^2 \end{gathered}$$

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