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. type your answer in the box. you may use numbers, a decimal point (.), and/or a negative sign (-) in your answer. in one design being considered for the container shaped like a cylinder, the container will have a height of 12 inches. what will be the radius of the container, to the nearest tenth of an inch?

Explanation:

Step1: Recall the volume formula for a cylinder

The volume formula for a cylinder is $V=\pi r^{2}h$, where $V$ is the volume, $r$ is the radius and $h$ is the height. We know that $V = 258\frac{3}{4}=\frac{258\times4 + 3}{4}=\frac{1032+3}{4}=\frac{1035}{4}$ cubic - inches and $h = 12$ inches.

Step2: Substitute the known values into the formula

Substituting into $V=\pi r^{2}h$, we get $\frac{1035}{4}=\pi r^{2}\times12$.

Step3: Solve for $r^{2}$

First, simplify the equation $\frac{1035}{4}=12\pi r^{2}$. Then $r^{2}=\frac{1035}{4\times12\pi}$. Calculate $\frac{1035}{4\times12\pi}=\frac{1035}{48\pi}$. Using $\pi\approx3.14$, we have $r^{2}=\frac{1035}{48\times3.14}=\frac{1035}{150.72}\approx6.87$.

Step4: Solve for $r$

Take the square - root of both sides: $r=\sqrt{r^{2}}$. So $r=\sqrt{6.87}\approx2.6$ inches.

Answer:

$2.6$