Question

a loaf of bread can be modeled by a rectangular prism topped with half a right cylinder. ariany 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 volume formula for a rectangular prism is \(V = l\times w\times h\). Here, \(l = 17\) in, \(w = 5\) in, \(h = 6\) in.
\(V_{prism}=17\times5\times6 = 510\) in³.

Step2: Calculate the volume of the half - cylinder

The diameter of the cylinder is \(d = 5\) in (so the radius \(r=\frac{d}{2}=\frac{5}{2}=2.5\) in), and the height (length) of the cylinder \(h = 17\) in. The volume formula for a full - cylinder is \(V=\pi r^{2}h\). For a half - cylinder, \(V_{half - cylinder}=\frac{1}{2}\pi r^{2}h\).
Substitute \(r = 2.5\) in and \(h = 17\) in:
\(V_{half - cylinder}=\frac{1}{2}\times\pi\times(2.5)^{2}\times17=\frac{1}{2}\times\pi\times6.25\times17=\frac{106.25\pi}{2}\approx\frac{106.25\times3.14}{2}=166.8125\) in³.

Step3: Calculate the total volume of the loaf

\(V = V_{prism}+V_{half - cylinder}\).
\(V=510 + 166.8125=676.8125\approx676.8\) in³.

Answer:

\(676.8\) in³