Question

elizabeth and lillian have cube - shaped bins to store their items on shelves. the volume of each storage cube is 415 cubic inches. the length of each side of the cube must be between 7 and 8 inches. elizabeth thinks the length of the side of the cube is closer to 7 inches and lillian thinks the length of the side of the cube is closer to 8 inches. who is correct? select choice is correct.

Explanation:

Step1: Recall volume formula for cube

The volume formula of a cube is $V = s^{3}$, where $s$ is the side - length of the cube. We need to find $s$ given $V = 415$ cubic inches, so $s=\sqrt[3]{V}=\sqrt[3]{415}$.

Step2: Calculate $7^{3}$ and $8^{3}$

$7^{3}=7\times7\times7 = 343$ and $8^{3}=8\times8\times8 = 512$.

Step3: Compare distances

Find the distance between 415 and 343: $d_1=415 - 343=72$. Find the distance between 512 and 415: $d_2 = 512-415 = 97$. Since $72<97$, the side - length of the cube is closer to 7 inches.

Answer:

Elizabeth