Question

#4) 4 ft, 9 ft, 5 ft, 2 ft, 5 ft

Explanation:

Assuming the problem is to find the volume of this composite rectangular prism.

Step1: Analyze the composite shape

The composite shape can be thought of as two rectangular prisms. Let's find the dimensions of each. The first (top) prism: length = 5 ft, width = let's see, the total length is 9 ft? Wait, no, maybe the base is 9 ft in length, 5 ft in width, and the height of the bottom part: total height is 4 ft, top part height is 2 ft, so bottom part height is \( 4 - 2 = 2 \) ft. Wait, maybe better to split into two parts: one with dimensions \( 9 \) ft (length), \( 5 \) ft (width), \( 2 \) ft (height) and another with dimensions \( 5 \) ft (length), \( 5 \) ft (width)? Wait, no, looking at the diagram: the top prism has length 5 ft, width (let's say the same as the bottom's width? Wait, maybe the correct split is: the bottom part is a rectangular prism with length 9 ft, width 5 ft, height \( 4 - 2 = 2 \) ft. The top part is a rectangular prism with length 5 ft, width 5 ft, height 2 ft? Wait, no, maybe the length of the top is 5 ft, and the length of the bottom is 9 ft, but the width is 5 ft for both? Wait, perhaps the correct way is to calculate the volume of the larger rectangular prism (if there was no indentation) and then subtract the volume of the missing part, but maybe it's easier to add the two parts.

Wait, let's re-examine: The total height is 4 ft. The top prism has height 2 ft, length 5 ft, and width (let's assume the width is 5 ft? Wait, no, the bottom part: length 9 ft, width 5 ft, height \( 4 - 2 = 2 \) ft. The top part: length 5 ft, width 5 ft, height 2 ft? Wait, maybe not. Alternatively, the composite figure can be considered as two rectangular prisms:

1. First prism: length = 9 ft, width = 5 ft, height = 2 ft (bottom part)
2. Second prism: length = 5 ft, width = 5 ft, height = 2 ft (top part)

Wait, no, maybe the length of the top is 5 ft, and the length of the bottom is 9 ft, but the width is 5 ft for both. Wait, perhaps the correct dimensions are:

Bottom prism: length = 9 ft, width = 5 ft, height = \( 4 - 2 = 2 \) ft

Top prism: length = 5 ft, width = 5 ft, height = 2 ft

Wait, no, maybe the top prism has length 5 ft, width (let's say the same as the bottom's width, which is 5 ft), and height 2 ft. The bottom prism has length 9 ft, width 5 ft, height \( 4 - 2 = 2 \) ft. Wait, but then the total volume would be the sum of the two volumes.

Alternatively, maybe the original large prism (without the indentation) would have length 9 ft, width 5 ft, height 4 ft. Then the missing part is a rectangular prism with length \( 9 - 5 = 4 \) ft, width 5 ft, height 2 ft. Wait, that might make sense. Let's check:

Original volume (if no indentation): \( 9 \times 5 \times 4 = 180 \) cubic feet

Missing volume: length = \( 9 - 5 = 4 \) ft, width = 5 ft, height = 2 ft. So volume of missing part: \( 4 \times 5 \times 2 = 40 \) cubic feet

Then the volume of the composite figure is \( 180 - 40 = 140 \) cubic feet. Wait, but let's verify with the other method.

First method: two prisms.

Bottom prism: length 9 ft, width 5 ft, height \( 4 - 2 = 2 \) ft. Volume: \( 9 \times 5 \times 2 = 90 \) cubic feet

Top prism: length 5 ft, width 5 ft, height 2 ft. Volume: \( 5 \times 5 \times 2 = 50 \) cubic feet

Total volume: \( 90 + 50 = 140 \) cubic feet. Yes, that matches. So that's correct.

Step1: Calculate volume of bottom prism

The bottom prism has length \( l = 9 \) ft, width \( w = 5 \) ft, height \( h = 4 - 2 = 2 \) ft. The volume of a rectangular prism is \( V = l \times w \times h \).

So, \( V_{bottom} = 9 \times 5 \times 2 \)
\( V_{bottom} = 90 \) cubic feet

Step2: Calculate volume of top prism

The…

Answer:

The volume of the composite figure is \(\boxed{140}\) cubic feet.