Respuesta :
3) In general, a dilation is an enlargement of the sides of a shape, even if it is a 3D shape.
Furthermore, the volume of a prism is given by the formula
[tex]V=A_{\text{base}}\cdot h=l\cdot w\cdot h[/tex]Then,
[tex]V_{\text{new}}=3l\cdot3w\cdot3w=3^3(l\cdot w\cdot h)=27V_{initial}[/tex]Therefore,
[tex]\Rightarrow V_{\text{new}}=27\cdot(270)=7290[/tex]The answer to part 3) is 7290 m^3
4) Due to similar reasoning, in general, the area of a shape is given by
[tex]A=l\cdot w[/tex]If we apply a dilation to that area,
[tex]\Rightarrow A_{\text{new}}=kl\cdot kw=k^2A_{original}[/tex]Where k is the dilation factor.
Thus, in our case,
[tex]\begin{gathered} \Rightarrow A_{\text{new}}=(54)^2\cdot8=23328 \\ \text{and} \\ h_{\text{new}}=54\cdot6=324 \end{gathered}[/tex]Therefore,
[tex]\Rightarrow V_{\text{new}}=A_{\text{new}}\cdot h_{\text{new}}=23328\cdot324=7558272[/tex]The answer to part 4) is 7558272 cm^3
5) From the answer to question 3)
[tex]V_{\text{new}}=k^3\cdot V_{original}_{}[/tex]Thus,
[tex]\begin{gathered} \Rightarrow3125=k^3\cdot200 \\ \Rightarrow k^3=\frac{3125}{200}=\frac{125}{8} \\ \Rightarrow k=\frac{5}{2}=2.5 \\ \Rightarrow k=2.5 \end{gathered}[/tex]The answer to part 5) is 2.5
