The problem asks us to identify which of the given statements are correct, involving conversions between different units of area and volume. The given statements are: 1. $4 m^2 = 400 cm^2$

1. Problem Description

The problem asks us to identify which of the given statements are correct, involving conversions between different units of area and volume. The given statements are:

1. $4 m^2 = 400 cm^2$

2. $1.4 cm^2 > 14 mm^2$

3. $600 mm^3 < 0.06 cm^3$

4. $0.0032 m^3 = 3200 cm^3$

2. Solution Steps

We need to verify each statement separately:

1. $4 m^2 = 400 cm^2$

We know that $1 m = 100 cm$, so $1 m^2 = (100 cm)^2 = 10000 cm^2$. Therefore, $4 m^2 = 4 \times 10000 cm^2 = 40000 cm^2$. Thus, $4 m^2 = 400 cm^2$ is incorrect.

2. $1.4 cm^2 > 14 mm^2$

We know that $1 cm = 10 mm$, so $1 cm^2 = (10 mm)^2 = 100 mm^2$. Therefore, $1.4 cm^2 = 1.4 \times 100 mm^2 = 140 mm^2$. Thus, $140 mm^2 > 14 mm^2$, which means $1.4 cm^2 > 14 mm^2$ is correct.

3. $600 mm^3 < 0.06 cm^3$

We know that $1 cm = 10 mm$, so $1 cm^3 = (10 mm)^3 = 1000 mm^3$. Therefore, $0.06 cm^3 = 0.06 \times 1000 mm^3 = 60 mm^3$. Thus, $600 mm^3 < 60 mm^3$ is incorrect.

4. $0.0032 m^3 = 3200 cm^3$

We know that $1 m = 100 cm$, so $1 m^3 = (100 cm)^3 = 1000000 cm^3$. Therefore, $0.0032 m^3 = 0.0032 \times 1000000 cm^3 = 3200 cm^3$. Thus, $0.0032 m^3 = 3200 cm^3$ is correct.

3. Final Answer

$1.4 cm^2 > 14 mm^2$

$0.0032 m^3 = 3200 cm^3$