Question

determine the volume of a cube that has a side length of 7 feet.

Explanation:

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Problem 1: Cube Volume

Step1: Recall cube volume formula

Volume of cube: $V = s^3$, where $s$ = side length

Step2: Substitute $s=7$ feet

$V = 7^3 = 7 \times 7 \times 7$

Step3: Calculate the result

$7 \times 7 = 49$, $49 \times 7 = 343$

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Problem 2: Straws and Cups

Step1: Find LCM of 10 and 12

Prime factors: $10=2\times5$, $12=2^2\times3$
LCM = $2^2\times3\times5 = 60$

Step2: Calculate straw packs

$\text{Straw packs} = \frac{60}{10} = 6$

Step3: Calculate cup packs

$\text{Cup packs} = \frac{60}{12} = 5$

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Problem 3: Pet Store Number Line

Step1: Simplify the ratio

Dogs:Fish = $4:6 = 2:3$

Step2: Define base unit set

Base set: 2 dogs, 3 fish, total 5 animals

Step3: Map to number line

Mark intervals: 0 → 2 (dogs) → 5 (dogs+fish) → 10 (2x set) → ...

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Problem 4: Write the Expression

Step1: Identify sum first

Sum of 3 and 9: $(3 + 9)$

Step2: Multiply by 5

Expression: $5 \times (3 + 9)$

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Answer:

1. Volume of the cube: 343 cubic feet
2. - Total number to purchase: 60 (60 straws and 60 cups)

• Packs to purchase: 6 packs of straws, 5 packs of cups

1. Number line:

• Mark 0 as the start
• Mark 2 (label: Dogs)
• Mark 5 (label: Total Animals, 2 dogs + 3 fish)
• Extend with intervals of 2 (dogs) and 3 (fish) for larger sets

1. Expression: $5(3 + 9)$