The problem asks to find the total volume of a composite figure made of a square pyramid on top of a rectangular prism. The side length of the square base of the pyramid is 6.5 inches, and the height of the pyramid is 6.5 inches. The height of the rectangular prism is 3.2 inches, and the base of the prism is a square with side length 6.5 inches. We need to find the total volume of the composite figure, rounded to the nearest tenth.

1. Problem Description

The problem asks to find the total volume of a composite figure made of a square pyramid on top of a rectangular prism. The side length of the square base of the pyramid is 6.5 inches, and the height of the pyramid is 6.5 inches. The height of the rectangular prism is 3.2 inches, and the base of the prism is a square with side length 6.5 inches. We need to find the total volume of the composite figure, rounded to the nearest tenth.

2. Solution Steps

First, find the volume of the square pyramid.

The formula for the volume of a pyramid is:

$V_{pyramid} = \frac{1}{3} \cdot base\_area \cdot height$

The base area of the square pyramid is:

$base\_area = side^2 = (6.5)^2 = 42.25 \text{ in}^2$

The height of the pyramid is 6.5 inches. Therefore, the volume of the pyramid is:

$V_{pyramid} = \frac{1}{3} \cdot 42.25 \cdot 6.5 = \frac{274.625}{3} \approx 91.54167 \text{ in}^3$

Next, find the volume of the rectangular prism.

The formula for the volume of a rectangular prism is:

$V_{prism} = length \cdot width \cdot height$

Since the base is a square, the length and width are the same. So,

$V_{prism} = side^2 \cdot height = (6.5)^2 \cdot 3.2 = 42.25 \cdot 3.2 = 135.2 \text{ in}^3$

Finally, find the total volume by adding the volumes of the pyramid and the prism:

$V_{total} = V_{pyramid} + V_{prism} = 91.54167 + 135.2 = 226.74167 \text{ in}^3$

Round the total volume to the nearest tenth:

$V_{total} \approx 226.7 \text{ in}^3$

3. Final Answer

226.7 $in^3$