Question

Determine the volume of the three-dimensional
figure.

Answer 1

`\huge\boxed{V=288\ in^3}`

Explanation:

The formula of a volume of a prism:

`V=BH`

where

B - area of a base

H - height of a prism

In the base we have the trapezoid.

The formula of an area of a trapezoid:

`A=(b_1+b_2)/(2)\cdot h`

Where

`b_1,\ b_2` - bases

`h` - height of a trapezoid

From the picture we have:

`b_1=16\ in,\ b_2=8\ in,\ h=6\ in`

Substitute:

`B=(16+8)/(2)\cdot6=(24)/(2)\cdot6=12\cdot6=72\ in^2`

Substitute it and H = 4 in to the formula of a volume of a prism:

`V=(72)(4)=288\ in^3`

Answer 2

288 cubic inch

Explanation:

Top and bottom bases are trapezoid of same dimensions and height is 4 in.

Therefore,

`volume \\ = area \: of \: trapezoid * height \\ = \{(1)/(2) (16 + 8) * 6 \} * 4 \\ = 24 * 6 * 2 \\ = 48 * 6 \\ = 288 \: {in}^(3) \\`