Question

Which prism has a greater volume?

Prism A has a length of 4, height of 5, and width of 4. Prism B has a length of 3, height of 7, and width of 3.
Prism A has 17 more cubic units of volume than prism B.
Prism A has 7 more cubic units of volume than prism B.
Prism B has 3 more cubic units of volume than prism A.
Prism B has 8 more cubic units of volume than prism A.

Answer 1

To determine which prism has a greater volume, we need to calculate the volumes of both Prism A and Prism B using the formula for the volume of a rectangular prism, which is:

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

**Calculating Volume of Prism A:**

For Prism A:
- Length = 4
- Height = 5
- Width = 4

\[
\text{Volume of Prism A} = 4 \times 4 \times 5 = 80 \text{ cubic units}
\]

**Calculating Volume of Prism B:**

For Prism B:
- Length = 3
- Height = 7
- Width = 3

\[
\text{Volume of Prism B} = 3 \times 3 \times 7 = 63 \text{ cubic units}
\]

**Comparison of Volumes:**
- Volume of Prism A = 80 cubic units
- Volume of Prism B = 63 cubic units

Now we find the difference in volume:

\[
\text{Difference} = \text{Volume of Prism A} - \text{Volume of Prism B} = 80 - 63 = 17 \text{ cubic units}
\]

Thus, Prism A has **17 more cubic units** of volume than Prism B.

Based on this calculation, the answer is:
**Prism A has 17 more cubic units of volume than Prism B.**