Question

a cereal company is designing containers for a new type of cereal. each container will be shaped like either a rectangular prism or a cylinder and needs to have a volume of 258\frac{3}{4} cubic inches. in one design being considered for the containers shaped like a rectangular prism, each container will have a height of 11\frac{1}{2} inches and length of 7\frac{1}{2} inches. what will be the width, in inches, of the container?
a. 3
b. 4
c. 14
d. 15

Explanation:

Step1: Recall volume formula for rectangular prism

The volume formula for a rectangular prism is $V = l\times w\times h$, where $V$ is volume, $l$ is length, $w$ is width and $h$ is height. We need to solve for $w$. So, $w=\frac{V}{l\times h}$.

Step2: Convert mixed - numbers to improper fractions

$V = 258\frac{3}{4}=\frac{258\times4 + 3}{4}=\frac{1032+3}{4}=\frac{1035}{4}$ inches³, $h = 11\frac{1}{2}=\frac{11\times2+1}{2}=\frac{22 + 1}{2}=\frac{23}{2}$ inches, $l=7\frac{1}{2}=\frac{7\times2 + 1}{2}=\frac{14+1}{2}=\frac{15}{2}$ inches.

Step3: Calculate $l\times h$

$l\times h=\frac{15}{2}\times\frac{23}{2}=\frac{15\times23}{4}=\frac{345}{4}$ inches².

Step4: Calculate $w$

$w=\frac{V}{l\times h}=\frac{\frac{1035}{4}}{\frac{345}{4}}=\frac{1035}{4}\times\frac{4}{345}=3$ inches.

Answer:

A. 3