Question

you were painting a room in your house. unfortunately, you lost the lid to the 5 - gallon bucket of paint, but you only used half of the paint. you want to save the paint, so you plan on transferring it to a new container. the new container is shaped like a rectangular prism. if there are originally 1,155 cubic inches of paint in the 5 - gallon bucket, is your container big enough to fit the paint that is left over? remember that half the paint is left in the bucket.
a. yes, the container is big enough. there is 577.5 cubic inches of paint left and the new container is 960 cubic inches.
b. yes, the container is big enough. there is 577.5 cubic inches of paint left and the new container is 480 cubic inches.
c. no, the container is not big enough. there is 577.5 cubic inches of paint left and the new container is 960 cubic inches.
d. no, the container is not big enough. there is 577.5 cubic inches of paint left and the new container is 480 cubic inches.

Explanation:

Step1: Calculate remaining paint volume

Since half of the paint is left and originally there are 1155 cubic - inches of paint, the remaining paint volume $V_{paint}=\frac{1155}{2}=577.5$ cubic inches.

Step2: Calculate volume of new container

The volume formula for a rectangular prism is $V = l\times w\times h$. Given $l = 12$ inches, $w = 8$ inches and $h = 5$ inches, then $V_{container}=12\times8\times5=480$ cubic inches.

Step3: Compare volumes

Since $V_{paint}=577.5$ cubic inches and $V_{container}=480$ cubic inches, and $577.5>480$, the container is not big enough.

Answer:

d. No, the container is not big enough. There is 577.5 cubic inches of paint left and the new container is 480 cubic inches.