Question

beatrice is using a cylinder shape container to hold 52 in³ of liquid. the height of the container is 4 inches tall. what is the best approximation for the radius of the container? 2.0 in. 2.5 in. 3.4 in. 6.5 in. calculator

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.

Step2: Substitute the given values into the formula

We know that \(V = 52\space in^{3}\) and \(h=4\space in\). Substituting these into the formula \(V=\pi r^{2}h\), we get \(52=\pi r^{2}\times4\).

Step3: Solve for \(r^{2}\)

First, simplify the equation \(52 = 4\pi r^{2}\). Divide both sides by \(4\pi\). So, \(r^{2}=\frac{52}{4\pi}\). Since \(\pi\approx3.14\), then \(r^{2}=\frac{52}{4\times3.14}=\frac{52}{12.56}\approx4.14\).

Step4: Solve for \(r\)

Take the square - root of both sides. \(r=\sqrt{r^{2}}\), so \(r=\sqrt{4.14}\approx2.03\approx2.0\space in\) (when rounded to one decimal place).

Answer:

2.0 in.