Question

Please help me out with this one

answer choices :
- 3648
- 2632
- 1387
- 2109

Answer 1

Hello!

The answer is:

The total volume is equal to:
`2622in^(3)`

Why?

To calculate the total volume of the composite figure, we need to calculate the volume of both of the figures that creates the composite figure.

So, calculating we have:

First figure:

The first figure has a triangular base (side for this case) and height, to find its volume, we just need to calculate the area of its base and then, multiply it by its height.

We are given that:

`base_(height)=9in\\base_(base)=12in\\length=19in`

Calculating the area of the side/base, we have:

`A=(b*h)/(2)`

`A=(12in*9in)/(2)=54in^(2)`

Now, calculating the volume, we have:

`Volume_(1)=Area*Length\\\\Volume_(1)=54in^(2)*19in=1026in^(3)`

Second figure:

The second figure is a rectangle, we can calculate its volume using the following formula:

`Volume_2=base*height*width\\\\Volume_2=12in*7in*19in=1596in^(3)`

Hence, we can calculate the total volume by adding the first volumen and the second volume:

`TotalVolume=Volume_1+Volume_2\\\\TotalVolume=1026in^(3) +1596in^(3)=2622in^(3)`

The total volume is equal to
`2622in^(3)`

Have a nice day!

Answer 2

`V = 2622\ in ^ 3`

Explanation:

We have a composite figure, therefore the volume of the figure will be the sum of the volume of both figures.

The volume of the rectangular prism is the product of its length by its width by its height

`V_r = 7 * 12 * 19\\\\V_r = 1596\ in^3`

The volume of the triangular prism is

`V_t = A_b * l`

Where
`A_b` is the area of the triangular base and l is the length

`A_b = 0.5 * 9 * 12 = 54\ in^2`

`V_t = 0.54 * 19 = 1026\ in^3`

Finally

`V = 1596 + 1026`

`V = 2622\ in ^ 3`