Question

1. carrie is packing her clothes in moving boxes that are in the shape of a cube. each box has a volume of 3 cubic feet. the moving truck has shelves that are 12 inches in height. will the moving boxes fit? explain.
2. construct an argument explain how you could estimate $sqrt3{20}$ to the nearest integer.

Explanation:

for Question 16:

Step1: Find side - length of cube box

The volume formula for a cube is $V = s^{3}$, where $V$ is volume and $s$ is side - length. Given $V = 3$ cubic feet, then $s=\sqrt[3]{3}$ feet.

Step2: Convert units

1 foot = 12 inches. So $s=\sqrt[3]{3}\times12$ inches. Since $\sqrt[3]{3}\approx1.44$, then $s\approx1.44\times12 = 17.28$ inches.

Step3: Compare with shelf height

The shelf height is 12 inches. Since $17.28>12$, the boxes will not fit.

for Question 17:

Step1: Find perfect - cube bounds

We know that $2^{3}=8$ and $3^{3}=27$.

Step2: Determine approximation

Since 20 is closer to 8 than to 27, $\sqrt[3]{20}\approx2$.

Answer:

for Question 16:
No.