Volume of Cubes - Math worksheet with problems to calculate cube volume using side lengths.

Let's solve the problem step by step based on the worksheet titled "Volume - Cube".

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A) Find the volume of each cube.

We are given three cubes with side lengths labeled. The formula for the volume of a cube is:

> Volume = side length³
> or
> V = s³

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#### 1)
Cube with side length = 3 units

$$
V = 3^3 = 3 \times 3 \times 3 = 27
$$

✔ Volume = 27 cubic units

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#### 2)
Cube with side length = 4 ft

$$
V = 4^3 = 4 \times 4 \times 4 = 64
$$

✔ Volume = 64 cubic feet (ft³)

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#### 3)
Cube with side length = 5 in

$$
V = 5^3 = 5 \times 5 \times 5 = 125
$$

✔ Volume = 125 cubic inches (in³)

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B) Find the volume of each cube from the given side length.

Again, use $ V = s^3 $

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#### 4) Side length = 32 in

$$
V = 32^3 = 32 \times 32 \times 32
$$

First: $ 32 \times 32 = 1024 $
Then: $ 1024 \times 32 $

Break it down:
- $ 1000 \times 32 = 32,000 $
- $ 24 \times 32 = 768 $
- Total = $ 32,000 + 768 = 32,768 $

✔ Volume = 32,768 in³

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#### 5) Side length = 17 ft

$$
V = 17^3 = 17 \times 17 \times 17
$$

First: $ 17 \times 17 = 289 $
Then: $ 289 \times 17 $

Break it down:
- $ 289 \times 10 = 2,890 $
- $ 289 \times 7 = 2,023 $
- Add: $ 2,890 + 2,023 = 4,913 $

✔ Volume = 4,913 ft³

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#### 6) Side length = 25 ft

$$
V = 25^3 = 25 \times 25 \times 25
$$

First: $ 25 \times 25 = 625 $
Then: $ 625 \times 25 $

Break it down:
- $ 625 \times 20 = 12,500 $
- $ 625 \times 5 = 3,125 $
- Add: $ 12,500 + 3,125 = 15,625 $

✔ Volume = 15,625 ft³

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#### 7) Side length = 39 yd

$$
V = 39^3 = 39 \times 39 \times 39
$$

First: $ 39 \times 39 = 1,521 $
Then: $ 1,521 \times 39 $

Break it down:
- $ 1,521 \times 30 = 45,630 $
- $ 1,521 \times 9 = 13,689 $
- Add: $ 45,630 + 13,689 = 59,319 $

✔ Volume = 59,319 yd³

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8) A cubical gift box has a side length of 20 inches. What is the volume?

$$
V = 20^3 = 20 \times 20 \times 20 = 8,000
$$

✔ Volume = 8,000 in³

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✔ Final Answers:

#### Part A:
1) 27
2) 64 ft³
3) 125 in³

#### Part B:
4) 32,768 in³
5) 4,913 ft³
6) 15,625 ft³
7) 59,319 yd³
8) 8,000 in³

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🔍 Explanation Summary:

- The volume of a cube is always calculated as side × side × side, or $ s^3 $.
- Units must be consistent and included in the final answer (e.g., in³, ft³, etc.).
- When multiplying large numbers, breaking them into smaller parts helps avoid errors.

Let me know if you'd like this in a printable format or need help visualizing the cubes!