To find:
a. The volume of the prism on the right.
b. The surface area of the prism on the right.
c. Find the height of the prism on the right.
Solution:
a.
It is known that the ratio of the volume of two similar figures is the ratio of the cube of their corresponding sides.
Let the volume of the prism on the right be V. So,
[tex]\begin{gathered} \frac{343}{V}=\frac{7^3}{4^3} \\ \frac{343}{V}=\frac{343}{64} \\ V=64cm^3 \end{gathered}[/tex]
b.
It is known that the ratio of surface area of two similar figures is the ratio of the square of their corresponding sides.
Let the surface area of the prism on the right be S. So,
[tex]\begin{gathered} \frac{S}{588}=\frac{4^2}{7^2} \\ S=\frac{588\times16}{49} \\ S=\frac{9408}{49} \\ S=192cm^2 \end{gathered}[/tex]
c.
It is known that in similar figures the ratio of their corresponding sides are equal.
Let the height of the prism on the right be x. So,
[tex]\begin{gathered} \frac{x}{28}=\frac{4}{7} \\ x=16 \end{gathered}[/tex]
