Question

There is a rectangular prism that has a height of 8 1/4 in., a length of 6 3/4 in., and a width of 2 1/4 in. Lina says that the volume is 125 19/64 in.^3 and Siddarth says that the volume is 55 11/16 in.^3 . Who has the correct answer, and why?(1 point)

Responses
Lina is correct because she multiplied all three measurements by each other.
Siddarth is correct because he multiplied the height and length correctly.
They are both incorrect.
Siddarth is correct because he simplified his answer.

Answer 1

To determine who is correct, we need to calculate the volume of the rectangular prism using the formula for the volume, which is:

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

First, we convert the measurements to improper fractions for easier multiplication:

1. Height: \( 8 \frac{1}{4} = \frac{33}{4} \)
2. Length: \( 6 \frac{3}{4} = \frac{27}{4} \)
3. Width: \( 2 \frac{1}{4} = \frac{9}{4} \)

Now, we can calculate the volume:

\[
\text{Volume} = \frac{33}{4} \times \frac{27}{4} \times \frac{9}{4}
\]

First, multiply the numerators:

\[
33 \times 27 \times 9
\]

Calculating this step by step:

- \( 33 \times 27 = 891 \)
- Now, \( 891 \times 9 = 8019 \)

Next, multiply the denominators:

\[
4 \times 4 \times 4 = 64
\]

So we have:

\[
\text{Volume} = \frac{8019}{64}
\]

To convert this to a mixed number, divide \( 8019 \) by \( 64 \):

- \( 8019 \div 64 \approx 125.296875 \)

This means:

\[
8019 \div 64 = 125 \quad \text{with a remainder of } 19
\]

Thus, the volume can be expressed as:

\[
125 \frac{19}{64} \text{ in}^3
\]

Now let's compare this with Lina’s and Siddarth's answers:

- **Lina's answer:** \( 125 \frac{19}{64} \text{ in}^3 \) (correct)
- **Siddarth's answer:** \( 55 \frac{11}{16} \text{ in}^3 \) (incorrect)

Therefore, the correct response is:

**Lina is correct because she multiplied all three measurements by each other.**