Question

What is the scale factor, perimeter ratio, surface ratio, and the volume ratio?????????????????????????????

Answer 1

Answer:

Scale factor = $\frac{4}{9}$

Perimeter ratio = 4 : 9

Surface area ratio = 16 : 81

Volume ratio = 64 : 729

Step-by-step explanation:

Volume ratio = $\frac{\text{volume of small prism}}{\text{Volume of large prism}}$

                      = $\frac{128}{1458}$

                      = $\frac{64}{729}$

                      = 64 : 729

Scale factor = $\sqrt[3]{\frac{\text{volume of small prism}}{\text{Volume of large prism}}}$

                    = $\sqrt[3]{\frac{64}{729}}$

                    = $\frac{4}{9}$

Perimeter ratio = Scale factor

                         = $\frac{4}{9}$

                         = 4 : 9

Surface area ratio = (Scale factor)²

                              = $(\frac{4}{9})^{2}$

                              = $\frac{16}{81}$

                              = 16 : 81