Cell Surface Area to Volume Ratio Worksheet - Name: Date: Surface ... - Free Printable

Let’s solve each problem step by step. We’ll calculate Surface Area (SA), Volume, and then the SA:V ratio for each shape.

---

Problem 1: Cube with side = 4 cm

We’re told it’s a cube, so all sides are equal: L = W = H = 4 cm

→ Surface Area (SA)
Formula for cube: L × W × 6
= 4 × 4 × 6
= 16 × 6
= 96 cm²

→ Volume
Formula: L × W × H
= 4 × 4 × 4
= 16 × 4
= 64 cm³

→ SA:V Ratio
SA ÷ V = 96 ÷ 64
Simplify: divide both by 32 → 3 : 2
So, SA:V = 3:2

✔ Matches what’s given — good!

---

Problem 2: Rectangular prism (column) with L=10 cm, W=4 cm, H=4 cm

→ Surface Area (SA)
Formula: (L×H×2) + (W×H×2) + (L×W×2)
Plug in numbers:
= (10×4×2) + (4×4×2) + (10×4×2)
= (80) + (32) + (80)
= 80 + 32 = 112; 112 + 80 = 192 cm²

→ Volume
Formula: L × W × H
= 10 × 4 × 4
= 40 × 4
= 160 cm³

→ SA:V Ratio
SA ÷ V = 192 ÷ 160
Simplify: divide both by 32 → 6 : 5
So, SA:V = 6:5

✔ Matches what’s given — correct!

---

Problem 3: Rectangular prism with L=6 cm, W=4 cm, H=4 cm

→ Surface Area (SA)
Formula: (L×H×2) + (W×H×2) + (L×W×2)
= (6×4×2) + (4×4×2) + (6×4×2)
= (48) + (32) + (48)
= 48 + 32 = 80; 80 + 48 = 128 cm²

→ Volume
Formula: L × W × H
= 6 × 4 × 4
= 24 × 4
= 96 cm³

→ SA:V Ratio
SA ÷ V = 128 ÷ 96
Simplify: divide both by 32 → 4 : 3
So, SA:V = 4:3

✔ Matches what’s given — perfect!

---

All three problems have been checked and match the provided answers. The calculations are correct.

Final Answer:
All given answers are correct:
1. SA = 96, Volume = 64, SA:V = 3:2
2. SA = 192, Volume = 160, SA:V = 6:5
3. SA = 128, Volume = 96, SA:V = 4:3