Question

use the rules for working with measurements to give your answer to the appropriate accuracy and/or precision.
find the volume of the figure (in ( m^{3} )).
need help?

Explanation:

Step1: Find the height of the pyramid using Pythagorean theorem

Let's first find the height \(h\) of the pyramid. The base of the right - triangle (formed to find the height) has a length \(l=\frac{18.4}{2}=9.2\) m. Using the Pythagorean theorem \(h = \sqrt{16.4^{2}-9.2^{2}}\).

$$h=\sqrt{(16.4 + 9.2)(16.4 - 9.2)}=\sqrt{25.6\times7.2}=\sqrt{184.32}\approx13.576$$

Step2: Calculate the volume of the pyramid

The formula for the volume of a pyramid is \(V=\frac{1}{3}Bh\), where \(B\) is the area of the base. The base is a rectangle with \(B = 10.2\times18.4=187.68\) \(m^{2}\).

$$V=\frac{1}{3}\times187.68\times13.576$$

$$V = 62.56\times13.576\approx849$$

Answer:

\(849\)