A metal sheet is 1 m long and 10 cm wide. Its mass is 22 g and its density is 8.8 g/cm³. Is it suitable for use if its thickness must be greater than 0.0022 cm? Also, determine if the metal is pure, g

The length of the sheet is $1 \text{ m}$, which is $100 \text{ cm}$.
The mass of the sheet is $22 \text{ g}$ and its density is $8.8 \text{ gcm}^{-3}$.
The formula for volume is $V = \frac{\text{Mass}}{\text{Density}}$.

The volume of a rectangular sheet is $V = \text{Length} \times \text{Width} \times \text{Thickness}$.
We can rearrange this to find the thickness: $\text{Thickness} = \frac{V}{\text{Length} \times \text{Width}}$.

The hint states that for the metal sheet to be suitable, its thickness should be greater than $0.0022 \text{ cm}$.
Since $0.0025 \text{ cm} > 0.0022 \text{ cm}$, the metal sheet is suitable.
The metal sheet is suitable.

The initial water level was $50 \text{ cm}^3$, and it rose to $55.7 \text{ cm}^3$ after the block was placed in the cylinder. The volume of the block is the difference in water levels.

The mass of the metal block is $45 \text{ g}$.
The formula for density is $\rho = \frac{\text{Mass}}{\text{Volume}}$.

The hint states that the density of the pure metal is $7.9 \text{ gcm}^{-3}$.
The calculated density of the unknown metal block is approximately $7.89 \text{ gcm}^{-3}$.
Since $7.89 \text{ gcm}^{-3}$ is very close to $7.9 \text{ gcm}^{-3}$, the metal used by the student is considered pure.
The metal used by the student is pure.