Question

pre-algebra ic sem 2 fall 2025
two - and three - dimensional geometry
which equation shows how to determine the volume of the tent?
$v = 7(8)(12)+\frac{1}{3}(2)(8)(12)$
$v = 7(8)(12)+\frac{1}{3}(2)(7)(12)$
$v = 7(8)(12)+\frac{1}{2}(2)(7)(12)$
$v = 7(8)(12)+\frac{1}{2}(2)(8)(12)$

Explanation:

Step1: Calculate the volume of the rectangular prism

The volume formula for a rectangular prism is \(V = l\times w\times h\). Here, \(l = 12\) feet, \(w = 8\) feet, \(h = 7\) feet. So the volume of the rectangular - prism part is \(V_{prism}=7\times8\times12\).

Step2: Calculate the volume of the pyramid

The volume formula for a pyramid is \(V=\frac{1}{3}Bh\), where \(B\) is the base area. The base of the pyramid is a rectangle with length \(l = 12\) feet and width \(w = 8\) feet (\(B = 12\times8\)), and the height \(h = 2\) feet. So the volume of the pyramid part is \(V_{pyramid}=\frac{1}{3}\times(12\times8)\times2\).

Answer:

\(V = 7(8)(12)+\frac{1}{3}(2)(8)(12)\)