Question

the solid glass award that jillian was given has a total height of 15 inches as shown. what is the total volume of glass used to make the award? 204 in³ 120 in³ 168 in³ 152 in³

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, \(l = 6\) in, \(w = 4\) in, \(h = 2\) in. So \(V_{prism}=6\times4\times2=48\) \(in^{3}\).

Step2: Calculate the height of the pyramid

The total height of the award is \(15\) in. The height of the prism is \(2\) in. So the height of the pyramid \(h_{pyramid}=15 - 2=13\) in.

Step3: Calculate the volume of the pyramid

The formula for the volume of a pyramid is \(V=\frac{1}{3}Bh\), where \(B\) is the base area. The base of the pyramid is the same as the base of the prism, \(B = 6\times4 = 24\) \(in^{2}\). Then \(V_{pyramid}=\frac{1}{3}\times24\times13 = 104\) \(in^{3}\).

Step4: Calculate the total volume

The total volume \(V = V_{prism}+V_{pyramid}\). So \(V=48 + 104=152\) \(in^{3}\).

Answer:

\(152\ in^{3}\)