Cantilevers 81937

Calculate a prism's volume and surface area with a base of a right triangle with cantilevers of length 40 and 43 cm. The height of the prism is 60 cm.

Correct answer:

V =  51600 cm³
S =  10223.6912 cm²

Step-by-step explanation:

$$\begin{gathered} a=40\text{cm} \\ b=43\text{cm} \\ h=60\text{cm} \\ {S}_1=\frac{a\cdot b}{2}=\frac{40\cdot 43}{2}=860{\text{cm}}^2 \\ V=S_1\cdot h=860\cdot 60=51600{\text{cm}}^3 \end{gathered}$$

$$\begin{gathered} c=\sqrt{a^2+b^2}=\sqrt{40^2+43^2}=\sqrt{3449}\text{cm}\doteq 58.7282\text{cm} \\ o=a+b+c=40+43+58.7282\doteq 141.7282\text{cm} \\ {S}_2=o\cdot h=141.7282\cdot 60\doteq 8503.6912{\text{cm}}^2 \\ S=2\cdot S_1+S_2=2\cdot 860+8503.6912=10223.6912{\text{cm}}^2 \end{gathered}$$

Try another example