Question

A loaf of bread can be modeled by a rectangular prism topped with half a right cylinder. Nevaeh measures the dimensions of the prism as 4 in by 5 in by 16 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.)

Answer 1

The volume of the loaf modeled by a rectangular prism topped with half a right cylinder is 477 cubic units.

What is the volume of the loaf?

Volume of the loaf = volume of a rectangular prism + volume of half a right cylinder

Length = 16

Width = 5

Height = 4

Volume of rectangular prism = Length × Width × Height

= 16 × 5 × 4

= 320 cubic units

Radius, r = 5/2

= 2.5

Height, h = 16

Volume of half a right cylinder = ½ × π × r² × h

= ½ × 3.14 × 2.5² × 16

= ½ × 3.14 × 6.25 × 16

= 157 cubic units

Hence,

Volume of the loaf = volume of a rectangular prism + volume of half a right cylinder

= 320 cubic units + 157 cubic units

= 477 cubic units

Answer 2

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.

Step-by-step explanation:

Consider the formula to find the radius.

`r=(d)/(2)`

Substitute d =5 in the formula.

`r=(5)/(2)=2.5\text{ inches.}`

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.

`V_1=(1)/(2)\pi r^2h`

Substitute r =2.5 and h =16 in the formula.

`V_1=(1)/(2)*3.14*2.5^2*16`

`V_1=157\text{ inches}^3`

Consider the formula to find the volume of the rectangular prism.

`V_2=l* w* h`

Substitute l =5, w =16 anf h =4 in the formula.

`V_2=5*16*4`

`V_2=320inches^3`

The voume of the loaf is the volume of the half a right cylinder and the volume of the rectangular prism.

`V=V_1+V_2`
`V=157+320`

`V=477inches^3`

Final answer:

The volume of the loaf is 477.0 cubic inches.