Question
What is the calculation of the density of a wooden block with a length of 12 cm , width of 20 cm , height of 18 cm , and a mass of 20 kilograms?
(1 point)
Responses
5.89 g/cm3 5.89 g/cm3
4.63 g/cm3 4.63 g/cm3
463 g/cm3463 g/cm3
46.3 g/cm3
(1 point)
Responses
5.89 g/cm3 5.89 g/cm3
4.63 g/cm3 4.63 g/cm3
463 g/cm3463 g/cm3
46.3 g/cm3
Answers
GPT-4o mini
To calculate the density of the wooden block, you can use the formula:
\[
\text{Density} = \frac{\text{Mass}}{\text{Volume}}
\]
1. First, calculate the volume of the block. The formula for the volume of a rectangular prism is:
\[
\text{Volume} = \text{Length} \times \text{Width} \times \text{Height}
\]
Given:
- Length = 12 cm
- Width = 20 cm
- Height = 18 cm
\[
\text{Volume} = 12 \, \text{cm} \times 20 \, \text{cm} \times 18 \, \text{cm} = 4320 \, \text{cm}^3
\]
2. Next, we need the mass in grams since the options for density are in \( \text{g/cm}^3 \):
- Mass = 20 kg = 20,000 g (since 1 kg = 1000 g)
3. Now, we can calculate the density:
\[
\text{Density} = \frac{20000 \, \text{g}}{4320 \, \text{cm}^3} \approx 4.63 \, \text{g/cm}^3
\]
So, the density of the wooden block is approximately **4.63 g/cm³**.
The correct response is:
**4.63 g/cm³**
\[
\text{Density} = \frac{\text{Mass}}{\text{Volume}}
\]
1. First, calculate the volume of the block. The formula for the volume of a rectangular prism is:
\[
\text{Volume} = \text{Length} \times \text{Width} \times \text{Height}
\]
Given:
- Length = 12 cm
- Width = 20 cm
- Height = 18 cm
\[
\text{Volume} = 12 \, \text{cm} \times 20 \, \text{cm} \times 18 \, \text{cm} = 4320 \, \text{cm}^3
\]
2. Next, we need the mass in grams since the options for density are in \( \text{g/cm}^3 \):
- Mass = 20 kg = 20,000 g (since 1 kg = 1000 g)
3. Now, we can calculate the density:
\[
\text{Density} = \frac{20000 \, \text{g}}{4320 \, \text{cm}^3} \approx 4.63 \, \text{g/cm}^3
\]
So, the density of the wooden block is approximately **4.63 g/cm³**.
The correct response is:
**4.63 g/cm³**