Question

PLEASE HELP 50 POINTS

Answer 1

The volume of the solid is:

`408~\text{in}^(3)`

Explanation:

Step 1: Analyzing the cross-sectional area

Upon looking at the cross-sectional area, we can see that we can separate it into three different rectangles (as shown in the diagram).

The area of rectangles are given by:

`\text{Area}=\text{Length}* \text{Width}`

The length of the top rectangle is 7, and the width is 2, so substitute these values:

`\text{Area}=7*2\\\text{Area}=14`

The length of the middle rectangle is 8, and the width is 5, so substitute these values and calculate:

`\text{Area}=8*5\\\text{Area}=40`

The bottom rectangle is the same as the top rectangle, so it will have the same area as it:

`\text{Area}=14`

The area of the entire cross-sectional area will be the sum of all these areas:

`\text{Total Area}=14+40+14\\\text{Total Area}=68~\text{in}^(2)`

Step 2: Calculating the volume

The volume of any solid is given by:

`\text{Volume}=\text{Cross-sectional area}* \text{Length}`

We have obtained the cross-sectional area, and the length is
`6`.

Substitute these values into the formula:

`\text{Volume}=\text{Cross-sectional area}* \text{Length}\\\text{Volume}=68* 6\\\\\text{Calculate:}\\\text{Volume}=408~\text{in}^(3)`