Question

A sheet of glass has a density of 2.5 \dfrac{\text{g}}{\text{cm}^3}2.5 cm 3 g ​ 2, point, 5, start fraction, start text, g, end text, divided by, start text, c, m, end text, cubed, end fraction. What is the density of the glass in \dfrac{\text{kg}}{\text{m}^3} m 3 kg ​ start fraction, start text, k, g, end text, divided by, start text, m, end text, cubed, end fraction?

Answer 1

2,500

It works for me on Khan Academy December 2022

Answer 2

`\frac{\text{25,00 kg}}{\text{m}^3}`

Explanation:

We have been given that a sheet of glass has a density of
`2.5\frac{\text{g}}{\text{cm}^3}`. We are asked to find the density of the glass in
`\frac{\text{kg}}{\text{cm}^3}`.

We know that 1 meter equals so 100 cm.

`\text{ 1 m}^3=(\text{ 100 cm})^3`

`\text{ 1 m}^3=\text{ 1,000,000 cm}^3`

`2.5\frac{\text{g}}{\text{cm}^3}* \frac{\text{1,000,000 cm}^3}{\text{ 1 m}^3}}`

`\frac{\text{2.5 g}}{\text{m}^3}* 1,000,000`

`\frac{\text{25,00,000 g}}{\text{m}^3}`

We also know that 1 kg equals 1000 grams.

`\frac{\text{25,00,000 g}}{\text{m}^3}* \frac{\text{1 kg}}{1,000\text{ gm}}`

`\frac{\text{25,00 kg}}{\text{m}^3}`

Therefore, the density of the glass sheet is 2500 kg per cubic meter.