Question

find the side length of each square: area = 225 in² area = 81 ft² area = 36 m² side length = side length = side length = find the side length of each cube: v = 125 v = 27 v = 216 side length = side length = side length =

Explanation:

Step1: Recall square - area formula

The area formula of a square is $A = s^2$, where $A$ is the area and $s$ is the side - length. To find $s$, we use $s=\sqrt{A}$.

Step2: Calculate side - length of $225\text{ in}^2$ square

For $A = 225\text{ in}^2$, $s=\sqrt{225}=15$ in.

Step3: Calculate side - length of $81\text{ ft}^2$ square

For $A = 81\text{ ft}^2$, $s=\sqrt{81}=9$ ft.

Step4: Calculate side - length of $36\text{ m}^2$ square

For $A = 36\text{ m}^2$, $s=\sqrt{36}=6$ m.

Step5: Recall cube - volume formula

The volume formula of a cube is $V = s^3$, where $V$ is the volume and $s$ is the side - length. To find $s$, we use $s=\sqrt[3]{V}$.

Step6: Calculate side - length of volume $125$ cube

For $V = 125$, $s=\sqrt[3]{125}=5$.

Step7: Calculate side - length of volume $27$ cube

For $V = 27$, $s=\sqrt[3]{27}=3$.

Step8: Calculate side - length of volume $216$ cube

For $V = 216$, $s=\sqrt[3]{216}=6$.

Answer:

• Square with area $225\text{ in}^2$: Side Length = $15$ in
• Square with area $81\text{ ft}^2$: Side Length = $9$ ft
• Square with area $36\text{ m}^2$: Side Length = $6$ m
• Cube with volume $125$: Side Length = $5$
• Cube with volume $27$: Side Length = $3$
• Cube with volume $216$: Side Length = $6$