Answer:
A. [tex]\frac{25}{9}[/tex]
Step-by-step explanation:
We have been given that Cube A and Cube B are similar solids. The volume of cube A is 27 cubic inches, and the volume of cube B is 125 cubic inches. We are asked to find the the number of times the base area of cube b is larger than the base area of cube A.
We know that volume of cube with each side of [tex]x[/tex] units is equal to [tex]x^3[/tex].
First of all, we will find the each side of cube A and B as:
[tex]A^3=27[/tex]
[tex]\sqrt[3]{A^3} =\sqrt[3]{27}[/tex]
[tex]A=3[/tex]
[tex]B^3=125[/tex]
[tex]\sqrt[3]{B^3} =\sqrt[3]{125}[/tex]
[tex]B=5[/tex]
Now, we will find base area of both cubes as:
[tex]\frac{\text{Base area of cube B}}{\text{Base area of cube A}}=\frac{B^2}{A^2}[/tex]
[tex]\frac{\text{Base area of cube B}}{\text{Base area of cube A}}=\frac{5^2}{3^2}[/tex]
[tex]\frac{\text{Base area of cube B}}{\text{Base area of cube A}}=\frac{25}{9}[/tex]
Therefore, the base area of cube B is [tex]\frac{25}{9}[/tex] times larger than the base area of cube A.
