Question

find the volume of the figure shown below.
16 m
13 m
14.5 m
provide an answer accurate to the nearest hundredth.
label required

Explanation:

Step1: Identify the formula for the volume of a pyramid

The volume \( V \) of a pyramid is given by the formula \( V = \frac{1}{3}Bh \), where \( B \) is the area of the base and \( h \) is the height of the pyramid.

Step2: Calculate the area of the base

The base of the pyramid is a rectangle with length \( l = 14.5 \, \text{m} \) and width \( w = 13 \, \text{m} \). The area of a rectangle is \( B = l \times w \).
So, \( B = 14.5 \times 13 = 188.5 \, \text{m}^2 \).

Step3: Substitute the values into the volume formula

The height \( h \) of the pyramid is \( 16 \, \text{m} \). Substituting \( B = 188.5 \) and \( h = 16 \) into the volume formula:
\( V = \frac{1}{3} \times 188.5 \times 16 \)

Step4: Perform the calculation

First, calculate \( 188.5 \times 16 = 3016 \). Then, divide by 3: \( V = \frac{3016}{3} \approx 1005.333\ldots \)

Step5: Round to the nearest hundredth

Rounding \( 1005.333\ldots \) to the nearest hundredth gives \( 1005.33 \, \text{m}^3 \).

Answer:

\( 1005.33 \, \text{cubic meters} \) (or \( 1005.33 \, \text{m}^3 \))