Question

Determine the volume of the three-dimensional figure.

Answer 1

Answer:

288 cubic inch

Step-by-step explanation:

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

Therefore,

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

Answer 2

Answer:

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

Step-by-step 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:

$A=\dfrac{b_1+b_2}{2}\cdot h$

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:

$B=\dfrac{16+8}{2}\cdot6=\dfrac{24}{2}\cdot6=12\cdot6=72\ in^2$

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

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