Question

what is the volume of the rectangular prism? cubic unit(s)

Explanation:

Step1: Identify the formula for the volume of a rectangular prism

The volume \( V \) of a rectangular prism is given by the formula \( V = l \times w \times h \), where \( l \) is the length, \( w \) is the width, and \( h \) is the height.

Step2: Determine the dimensions from the figure and given information

From the problem and the figure, we can see that the length \( l = 3 \), the width \( w = 1 \), and the height \( h = 5 \)? Wait, no, looking at the handwritten part, it seems the dimensions are \( 3 \times 1 \times 5 \)? Wait, no, the handwritten calculation was \( 4 \times 2 \times 1 = 8 \), but maybe the figure has length 3, height 5, width 1? Wait, let's re-examine. Wait, the figure shows a rectangular prism made of unit cubes. Let's count the number of unit cubes along each edge. Looking at the figure, along the length (horizontal) there are 3 unit cubes, along the width (depth) there is 1 unit cube, and along the height (vertical) there are 5 unit cubes? Wait, no, maybe the handwritten part was a miscalculation. Wait, let's count the number of unit cubes. The figure has 3 columns (length), 1 row (width), and 5 layers (height). So the volume is \( 3 \times 1 \times 5 = 15 \)? Wait, no, maybe I misread. Wait, the handwritten text says "4x2x1=8", but the figure shows 3 columns, 5 rows vertically? Wait, maybe the correct dimensions are length 3, width 1, height 5. Wait, let's count the number of unit cubes. Each layer (front face) has 3 (length) x 5 (height) = 15 unit cubes, and since the width is 1, the total volume is 15 x 1 = 15. Wait, maybe the initial handwritten calculation was wrong. Wait, let's check the figure again. The figure shows a rectangular prism with 3 units along the length (x-axis), 1 unit along the width (y-axis), and 5 units along the height (z-axis). So the volume is \( 3 \times 1 \times 5 = 15 \) cubic units. Wait, but maybe the dimensions are different. Wait, the handwritten part says "4x2x1=8", but maybe that's a different problem. Wait, the user's figure: let's count the number of unit cubes. The front face has 3 columns (horizontal) and 5 rows (vertical), so 35=15, and since it's 1 unit deep (width), the volume is 151=15. So the correct volume is 15 cubic units.

Wait, maybe I made a mistake. Let's re-express. The formula for the volume of a rectangular prism is \( V = length \times width \times height \). From the figure, if we look at the number of unit cubes along each edge:

• Length: 3 (number of cubes along the horizontal direction)
• Width: 1 (number of cubes along the depth direction)
• Height: 5 (number of cubes along the vertical direction)

So \( V = 3 \times 1 \times 5 = 15 \).

Answer:

15