Let's solve each part step by step.
---
(a) Calculate the total surface area of cube 2
Cube 2 has side length =
2 cm
A cube has
6 faces, and each face is a square with area = side × side.
So,
> Surface area of one face = 2 cm × 2 cm =
4 cm²
> Total surface area = 6 × 4 cm² =
24 cm²
✔ Answer: 24 cm²
---
(b) Calculate the volume of cube 2
Volume of a cube = side³
> Volume = 2 cm × 2 cm × 2 cm =
8 cm³
✔ Answer: 8 cm³
---
(c) Calculate the surface area to volume ratio of cube 2
We are given the formula:
>
Surface area to volume ratio = surface area / volume
From (a) and (b):
> Surface area = 24 cm²
> Volume = 8 cm³
> Ratio = 24 / 8 =
3
So, the ratio is
3 : 1
✔ Answer: 3 : 1
---
💡 Why this matters in biology (osmosis context):
In cells or tissues like potato cubes,
osmosis (movement of water across a membrane) depends on how much surface area is available for water to enter/exit compared to the volume that needs to be hydrated.
-
Higher surface area to volume ratio → faster rate of osmosis (more exchange per unit volume).
- Cube 1 (1 cm side): SA:V = 6:1 → higher ratio → faster osmosis.
- Cube 2 (2 cm side): SA:V = 3:1 → lower ratio → slower osmosis.
This shows why smaller cells or structures often have more efficient exchange — they have relatively more surface area for their volume.
---
✔ Final Answers:
(a) Total surface area of cube 2 =
24 cm²
(b) Volume of cube 2 =
8 cm³
(c) Surface area to volume ratio of cube 2 =
3 : 1
Parent Tip: Review the logic above to help your child master the concept of surface area to volume ratio worksheet.
