Question

a loaf of bread can be modeled by a rectangular prism topped with half a right cylinder. ariany s measures the dimensions of the prism as 6 in by 5 in by 17 in. using those dimensions, find the volume of the loaf. round your answer to the nearest tenth if necessary. (note: diagram is not drawn to scale.)

Explanation:

Step1: Calculate the volume of the rectangular prism

The formula for the volume of a rectangular prism is \(V_{prism}=l\times w\times h\). Here, \(l = 17\) in, \(w=6\) in, \(h = 5\) in. So, \(V_{prism}=17\times6\times5=510\) in³.

Step2: Calculate the volume of the half - cylinder

The formula for the volume of a cylinder is \(V_{cylinder}=\pi r^{2}h\). For a half - cylinder, \(V_{half - cylinder}=\frac{1}{2}\pi r^{2}h\). The diameter of the half - cylinder is equal to the height of the prism, so \(d = 5\) in, \(r=\frac{d}{2}=2.5\) in, and \(h = 17\) in. Then \(V_{half - cylinder}=\frac{1}{2}\times\pi\times(2.5)^{2}\times17=\frac{1}{2}\times\pi\times6.25\times17=\frac{106.25\pi}{2}\approx166.9\) in³.

Step3: Calculate the total volume of the loaf

The total volume \(V = V_{prism}+V_{half - cylinder}\). So \(V=510 + 166.9=676.9\) in³.

Answer:

\(676.9\) in³