Question

what is the volume of the composite figure?
140 cubic inches
147 cubic inches
168 cubic inches
196 cubic inches
(image of a composite figure with a rectangular prism and a pyramid: rectangular prism has length 7 in, width 3 in, height 4 in; total height of composite figure is 12 in.)

Explanation:

Step1: Calculate the volume of the rectangular prism

The formula for the volume of a rectangular prism is \(V = l\times w\times h\). Here, \(l = 7\) in, \(w=3\) in, \(h = 4\) in.
\(V_{prism}=7\times3\times4=84\) cubic inches.

Step2: Calculate the height of the pyramid

The total height of the composite figure is \(12\) in. The height of the prism is \(4\) in. So the height of the pyramid \(h_{pyramid}=12 - 4=8\) in.

Step3: Calculate the volume of the pyramid

The formula for the volume of a pyramid is \(V=\frac{1}{3}lwh\). Using \(l = 7\) in, \(w = 3\) in, \(h = 8\) in.
\(V_{pyramid}=\frac{1}{3}\times7\times3\times8=56\) cubic inches.

Step4: Calculate the volume of the composite figure

Add the volumes of the prism and the pyramid. \(V = V_{prism}+V_{pyramid}\).
\(V=84 + 56=140\) cubic inches.

Answer:

140 cubic inches