prymid base of 16 mi center line 8 mi

What is the volume of the rectangular pyramid. Round answer to nearest hundreth in decimal form.

1 answer

To find the volume of a rectangular pyramid, you can use the formula:

\[ V = \frac{1}{3} \times B \times h \]

where \( V \) is the volume, \( B \) is the area of the base, and \( h \) is the height of the pyramid.

Given:

  • The base of the pyramid is a square with a side length of 16 miles. Therefore, the area \( B \) of the base is:

\[ B = \text{side} \times \text{side} = 16 , \text{mi} \times 16 , \text{mi} = 256 , \text{mi}^2 \]

  • The height \( h \) of the pyramid is given as 8 miles.

Now, plug these values into the volume formula:

\[ V = \frac{1}{3} \times 256 , \text{mi}^2 \times 8 , \text{mi} \]

Calculating the volume:

\[ V = \frac{1}{3} \times 2048 , \text{mi}^3 \]

\[ V = \frac{2048}{3} \approx 682.67 , \text{mi}^3 \]

So, the volume of the rectangular pyramid is approximately \( \boxed{682.67 , \text{mi}^3} \).