Given:
A loaf of bread is a rectangular prism topped with half a right cylinder.
The length of the rectangular prism, l = 5 inches.
The width of the rectangular prism, w = 16 inches.
The height of the rectangular prism, h = 4 inches.
The diameter of the half a right cylinder, d =5 inches,
The height of the half a right cylinder, h =16 inches,
Required:
We need to find the volume of the loaf of bread.
Explanation:
Consider the formula to find the radius.
[tex]r=\frac{d}{2}[/tex]Substitute d =5 in the formula.
[tex]r=\frac{5}{2}=2.5\text{ inches.}[/tex]The radius of the half a right cylinder, r=2.5 inches,
Consider the formula to find the volume of the half a right cylinder.
[tex]V_1=\frac{1}{2}\pi r^2h[/tex]Substitute r =2.5 and h =16 in the formula.
[tex]V_1=\frac{1}{2}\times3.14\times2.5^2\times16[/tex][tex]V_1=157\text{ inches}^3[/tex]Consider the formula to find the volume of the rectangular prism.
[tex]V_2=l\times w\times h[/tex]Substitute l =5, w =16 anf h =4 in the formula.
[tex]V_2=5\times16\times4[/tex][tex]V_2=320inches^3[/tex]The voume of the loaf is the volume of the half a right cylinder and the volume of the rectangular prism.
[tex]V=V_1+V_2[/tex][tex]V=157+320[/tex][tex]V=477inches^3[/tex]Final answer:
The volume of the loaf is 477.0 cubic inches.
