Question

1. cynthia has leftovers in a rectangular casserole dish that measures 8 inches by 12 inches by 2 inches tall. she estimates that approximately half the dishs capacity remains. below is a diagram of the casserole dish and food with dimensions. a. what volume of food is left in the dish? b. she stores the leftovers in a cylindrical container that measures 5 inches in diameter. what height will the food reach in the new container? round to the nearest inch.

Explanation:

Step1: Calculate volume of food in rectangular - dish

The food in the rectangular dish forms a rectangular prism with length $l = 12$ inches, width $w = 8$ inches and height $h = 1$ inch. The volume formula for a rectangular prism is $V=l\times w\times h$.
$V = 12\times8\times1=96$ cubic inches.

Step2: Find height of food in cylindrical container

The volume of a cylinder is $V=\pi r^{2}h$, where $r$ is the radius and $h$ is the height. The diameter of the cylindrical container is $d = 5$ inches, so the radius $r=\frac{d}{2}=\frac{5}{2}=2.5$ inches.
We know the volume of food $V = 96$ cubic inches. Substitute $V$ and $r$ into the cylinder - volume formula and solve for $h$.
$96=\pi\times(2.5)^{2}\times h$
$h=\frac{96}{\pi\times(2.5)^{2}}$
$h=\frac{96}{6.25\pi}$
$h=\frac{96}{6.25\times3.14}\approx\frac{96}{19.625}\approx5$ inches.

Answer:

a. 96 cubic inches
b. 5 inches