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?(1 point) Responses 50 cm 50 cm 5 cm 5 cm 3.2 cm 3.2 cm 25 cm

Answer 1

To find the width of the block, we can use the formula for density:

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

We can rearrange this to find the volume:

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

First, we need to convert the mass from kilograms to grams, since the density is given in grams per cubic centimeter:

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

Now using the density of 8 g/cm³:

\[
\text{Volume} = \frac{20,000 \text{ g}}{8 \text{ g/cm}^3} = 2500 \text{ cm}^3
\]

Next, we know the volume of a rectangular block is calculated as:

\[
\text{Volume} = \text{Length} \times \text{Width} \times \text{Height}
\]

Plugging in the values for length (5 cm) and height (10 cm):

\[
2500 \text{ cm}^3 = 5 \text{ cm} \times \text{Width} \times 10 \text{ cm}
\]

This simplifies to:

\[
2500 \text{ cm}^3 = 50 \text{ cm}^2 \times \text{Width}
\]

To find the width, divide both sides by 50 cm²:

\[
\text{Width} = \frac{2500 \text{ cm}^3}{50 \text{ cm}^2} = 50 \text{ cm}
\]

Thus, the width of the block is **50 cm**.