Math worksheet on volume and surface area of cubes.

Let's solve each problem step by step using the formulas for volume and surface area of a cube.

---

🔷 Cube Formulas:

- Volume (V) = $ s^3 $, where $ s $ is the edge length.
- Surface Area (SA) = $ 6s^2 $

---

## ✔ Problem 1a:

> The surface area of this cube is 96 square units. What is its edge length?

We are given:
- Surface Area = 96

Use the formula:
$$
SA = 6s^2
$$
$$
96 = 6s^2
$$
Divide both sides by 6:
$$
s^2 = \frac{96}{6} = 16
$$
Take the square root:
$$
s = \sqrt{16} = 4
$$

✔ Answer: Edge length = 4 units

---

## ✔ Problem 1b:

> The volume of this cube is 27 cubic units. What is its surface area?

Given:
- Volume = 27

Use:
$$
V = s^3
\Rightarrow 27 = s^3
\Rightarrow s = \sqrt[3]{27} = 3
$$

Now find surface area:
$$
SA = 6s^2 = 6(3)^2 = 6 \times 9 = 54
$$

✔ Answer: Surface Area = 54 square units

---

## ✔ Problem 2a:

> The volume of this cube is 27 cubic units. What is its edge length?

Same as 1b:
$$
s^3 = 27 \Rightarrow s = \sqrt[3]{27} = 3
$$

✔ Answer: Edge length = 3 units

---

## ✔ Problem 2b:

> The volume of this cube is 1 cubic unit. What is its surface area?

Given:
- Volume = 1 → $ s^3 = 1 $ → $ s = \sqrt[3]{1} = 1 $

Now compute surface area:
$$
SA = 6s^2 = 6(1)^2 = 6
$$

✔ Answer: Surface Area = 6 square units

---

📝 Final Answers:

| Problem | Answer |
|--------|--------|
| 1a | Edge length = 4 units |
| 1b | Surface area = 54 square units |
| 2a | Edge length = 3 units |
| 2b | Surface area = 6 square units |

Let me know if you'd like these explained visually or with diagrams!