Question

what is the volume of rectangular prism shown
3 1/2in 2 3/4 in 1 7/8 in

6 21/64 in^3
8 1/8 in ^3
18 3/64 in ^3
21 11/32 in ^3

Answer 1

To find the volume of a rectangular prism, you multiply its length, width, and height together.

Given the dimensions:

- Length = \(3 \frac{1}{2} \, \text{in} = \frac{7}{2} \, \text{in}\)
- Width = \(2 \frac{3}{4} \, \text{in} = \frac{11}{4} \, \text{in}\)
- Height = \(1 \frac{7}{8} \, \text{in} = \frac{15}{8} \, \text{in}\)

Now, we can calculate the volume:

\[
V = \text{Length} \times \text{Width} \times \text{Height}
\]
\[
V = \left(\frac{7}{2} \cdot \frac{11}{4} \cdot \frac{15}{8}\right)
\]

Calculating step by step:

1. Multiply the numerators:
\[
7 \cdot 11 \cdot 15 = 1155
\]

2. Multiply the denominators:
\[
2 \cdot 4 \cdot 8 = 64
\]

Putting it all together:
\[
V = \frac{1155}{64} \, \text{in}^3
\]

Now, let's convert this to a mixed number:

To convert \( \frac{1155}{64} \):

- Divide \( 1155 \) by \( 64 \):
\[
1155 \div 64 \approx 18.015625
\]

This means \( \frac{1155}{64} \) is \( 18 \) with a remainder. To find the remainder:
\[
1155 - (64 \cdot 18) = 1155 - 1152 = 3
\]

So,
\[
\frac{1155}{64} = 18 \frac{3}{64} \, \text{in}^3
\]

Thus, the volume of the rectangular prism is
\[
\boxed{18 \frac{3}{64} \, \text{in}^3}
\]

This corresponds to the option: **18 3/64 in³**.