Question

if ( l = 13.1 ) ft., ( w = 45.5 ) ft., and ( h = 33.6 ) ft., calculate the volume of the prism to the nearest whole cubic foot:
a ( 18 ) ft.³
b ( 811 ) ft.³
c ( 19,453 ) ft.³
d ( 20,027 ) ft.³

Explanation:

Step1: Recall the volume formula for a rectangular prism

The volume \( V \) of a rectangular prism is given by the formula \( V = l \times w \times h \), where \( l \) is the length, \( w \) is the width, and \( h \) is the height.

Step2: Substitute the given values into the formula

We are given \( l = 13.1 \, \text{ft} \), \( w = 45.5 \, \text{ft} \), and \( h = 33.6 \, \text{ft} \). Substituting these values into the formula, we get:

$$ V = 13.1 \times 45.5 \times 33.6 $$

Step3: Perform the multiplication step by step

First, multiply \( 13.1 \) and \( 45.5 \):

$$ 13.1 \times 45.5 = 596.05 $$

Then, multiply the result by \( 33.6 \):

$$ 596.05 \times 33.6 = 596.05 \times 33 + 596.05 \times 0.6 = 19669.65 + 357.63 = 20027.28 $$

Step4: Round to the nearest whole number

Rounding \( 20027.28 \) to the nearest whole number gives \( 20027 \).

Answer:

\( 20027 \, \text{ft}^3 \) (corresponding to option D: 20,027 ft.³)