Question

What is the width of a block with a density of 8 g/cm3 , a mass of 20 kilograms, a length of 5 centimeters, and a height of 10 centimeters?

Answer 1

To find the width of the block, we can start by using the formula for density:

\[
\text{Density} = \frac{\text{Mass}}{\text{Volume}}
\]

We need to convert mass from kilograms to grams, since the density is given in grams per cubic centimeter.

\[
20 \text{ kg} = 20,000 \text{ g}
\]

Now, let's denote the width of the block as \( w \) (in centimeters). The volume \( V \) of the block can be calculated using the formula for the volume of a rectangular prism:

\[
V = \text{Length} \times \text{Height} \times \text{Width} = L \times H \times w
\]

In this case, the length \( L \) is 5 cm, the height \( H \) is 10 cm, and we need to find the width \( w \). So, the volume can be expressed as:

\[
V = 5 \, \text{cm} \times 10 \, \text{cm} \times w = 50w \, \text{cm}^3
\]

Now, we can substitute the volume into the density formula:

\[
8 \, \text{g/cm}^3 = \frac{20,000 \, \text{g}}{50w}
\]

Now, cross-multiply to solve for \( w \):

\[
8 \cdot 50w = 20,000
\]

This simplifies to:

\[
400w = 20,000
\]

Now, divide both sides by 400 to isolate \( w \):

\[
w = \frac{20,000}{400} = 50 \, \text{cm}
\]

Thus, the width of the block is \( 50 \, \text{cm} \).