Question

1. what is the volume of this loaf of bread, assuming that the top part of the end of the loaf is a semi - circle? show your work.

(there is a diagram of a loaf of bread: the bottom part is a rectangle with length 11 cm, height 6 cm, and the length of the loaf is 20 cm; the top part is a semi - circle with diameter 11 cm. also, there is a hand - written formula: ( r=\frac{11}{2}=5.5 ))

Explanation:

Step1: Identify the shapes

The loaf consists of a rectangular prism and a half - cylinder (semi - circular prism).
For the rectangular prism: length \( l = 20\) cm, width \( w = 11\) cm, height \( h = 6\) cm.
For the half - cylinder: diameter \( d = 11\) cm, so radius \( r=\frac{11}{2}=5.5\) cm, length (same as the length of the rectangular prism) \( L = 20\) cm.

Step2: Volume of rectangular prism

The formula for the volume of a rectangular prism is \(V_{prism}=l\times w\times h\).
Substitute \(l = 20\), \(w = 11\), \(h = 6\) into the formula:
\(V_{prism}=20\times11\times6=1320\) \(cm^{3}\)

Step3: Volume of half - cylinder

The formula for the volume of a full cylinder is \(V_{cylinder}=\pi r^{2}h\) (here \(h\) is the length of the cylinder, which is \(L = 20\) cm). For a half - cylinder, the volume is \(V_{half - cylinder}=\frac{1}{2}\pi r^{2}L\).
Substitute \(r = 5.5\), \(L = 20\) and \(\pi\approx3.14\) into the formula:
\(V_{half - cylinder}=\frac{1}{2}\times3.14\times(5.5)^{2}\times20\)
First, calculate \((5.5)^{2}=30.25\)
Then, \(\frac{1}{2}\times3.14\times30.25\times20 = 3.14\times30.25\times10=3.14\times302.5 = 950.85\) \(cm^{3}\)

Step4: Total volume of the loaf

The total volume \(V = V_{prism}+V_{half - cylinder}\)
\(V=1320 + 950.85=2270.85\) \(cm^{3}\)

Answer:

The volume of the loaf of bread is \(2270.85\) cubic centimeters.