Question

Find the scale factor of a cube with volume 216 ft^3 to a cube with volume 1000 ft^3.

Answer 1

Answer:

Scale factor of  cube to the smaller cube is 5 : 3.

Step-by-step explanation:

Ratio of the volumes of two cubes = $\frac{\text{volume of large prism}}{\text{Volume of small prism}}$

                                                          = $\frac{1000}{216}$

                                                          = $\frac{125}{27}$

Scale factor of these cubes = $\sqrt[3]{\text{ratio of the volumes of the cubes}}$

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

                                              = $\sqrt[3]{\frac{125}{27} }$

                                              = $\frac{5}{3}$

                                              = 5 : 3

Therefore, scale factor of  cube to the smaller cube is 5 : 3.