Question
Which method would determine the volume of the prism shown below?
A rectangular prism with length of 5 centimeters, height of 2 and one-fourth centimeters, and width of 2 centimeters.
10 unit cubes and 10 one-quarter cubes gives 10 + (10 times one-fourth) as the volume.
20 unit cubes and 10 one-quarter cubes gives 20 + (10 times one-fourth) as the volume.
20 unit cubes and 10 one-quarter cubes gives 20 + (10 times one-half) as the volume.
10 unit cubes and 10 one-quarter cubes gives 10 + (10 times one-half) as the volume.
A rectangular prism with length of 5 centimeters, height of 2 and one-fourth centimeters, and width of 2 centimeters.
10 unit cubes and 10 one-quarter cubes gives 10 + (10 times one-fourth) as the volume.
20 unit cubes and 10 one-quarter cubes gives 20 + (10 times one-fourth) as the volume.
20 unit cubes and 10 one-quarter cubes gives 20 + (10 times one-half) as the volume.
10 unit cubes and 10 one-quarter cubes gives 10 + (10 times one-half) as the volume.
Answers
Answered by
GPT-4o mini
To determine the volume of a rectangular prism, you can use the formula:
\[
\text{Volume} = \text{Length} \times \text{Width} \times \text{Height}
\]
In this case, the dimensions of the prism are as follows:
- Length = 5 cm
- Width = 2 cm
- Height = 2.25 cm (which is \(2 \frac{1}{4}\) cm)
Now let's calculate the volume:
\[
\text{Volume} = 5 \, \text{cm} \times 2 \, \text{cm} \times 2.25 \, \text{cm}
\]
Calculating step-by-step:
1. **Calculate the area of the base (Length x Width):**
\[ 5 \times 2 = 10 \text{ cm}^2 \]
2. **Multiply by the height:**
\[ 10 \text{ cm}^2 \times 2.25 \text{ cm} = 22.5 \text{ cm}^3 \]
The volume of the prism is \(22.5 \text{ cm}^3\).
Now, let’s look at the options given in the problem:
1. **10 unit cubes and 10 one-quarter cubes gives** \(10 + (10 \times \frac{1}{4})\) as the volume.
2. **20 unit cubes and 10 one-quarter cubes gives** \(20 + (10 \times \frac{1}{4})\) as the volume.
3. **20 unit cubes and 10 one-quarter cubes gives** \(20 + (10 \times \frac{1}{2})\) as the volume.
4. **10 unit cubes and 10 one-quarter cubes gives** \(10 + (10 \times \frac{1}{2})\) as the volume.
To relate these options to the computed volume of \(22.5 \text{ cm}^3\):
- The first option gives \(10 + (10 \times \frac{1}{4}) = 10 + 2.5 = 12.5\).
- The second option gives \(20 + (10 \times \frac{1}{4}) = 20 + 2.5 = 22.5\). (This matches our calculation!)
- The third option gives \(20 + (10 \times \frac{1}{2}) = 20 + 5 = 25\).
- The fourth option gives \(10 + (10 \times \frac{1}{2}) = 10 + 5 = 15\).
Therefore, the correct choice for determining the volume of this prism is **"20 unit cubes and 10 one-quarter cubes gives 20 + (10 times one-fourth) as the volume."**
\[
\text{Volume} = \text{Length} \times \text{Width} \times \text{Height}
\]
In this case, the dimensions of the prism are as follows:
- Length = 5 cm
- Width = 2 cm
- Height = 2.25 cm (which is \(2 \frac{1}{4}\) cm)
Now let's calculate the volume:
\[
\text{Volume} = 5 \, \text{cm} \times 2 \, \text{cm} \times 2.25 \, \text{cm}
\]
Calculating step-by-step:
1. **Calculate the area of the base (Length x Width):**
\[ 5 \times 2 = 10 \text{ cm}^2 \]
2. **Multiply by the height:**
\[ 10 \text{ cm}^2 \times 2.25 \text{ cm} = 22.5 \text{ cm}^3 \]
The volume of the prism is \(22.5 \text{ cm}^3\).
Now, let’s look at the options given in the problem:
1. **10 unit cubes and 10 one-quarter cubes gives** \(10 + (10 \times \frac{1}{4})\) as the volume.
2. **20 unit cubes and 10 one-quarter cubes gives** \(20 + (10 \times \frac{1}{4})\) as the volume.
3. **20 unit cubes and 10 one-quarter cubes gives** \(20 + (10 \times \frac{1}{2})\) as the volume.
4. **10 unit cubes and 10 one-quarter cubes gives** \(10 + (10 \times \frac{1}{2})\) as the volume.
To relate these options to the computed volume of \(22.5 \text{ cm}^3\):
- The first option gives \(10 + (10 \times \frac{1}{4}) = 10 + 2.5 = 12.5\).
- The second option gives \(20 + (10 \times \frac{1}{4}) = 20 + 2.5 = 22.5\). (This matches our calculation!)
- The third option gives \(20 + (10 \times \frac{1}{2}) = 20 + 5 = 25\).
- The fourth option gives \(10 + (10 \times \frac{1}{2}) = 10 + 5 = 15\).
Therefore, the correct choice for determining the volume of this prism is **"20 unit cubes and 10 one-quarter cubes gives 20 + (10 times one-fourth) as the volume."**