Question

a factory designs cylindrical cans 10 cm in height to hold exactly 500 cm³ of liquid. which of the following best approximates the radius of these cans? choose 1 answer: a 4 cm b 8 cm c 12.5 cm d 15.9 cm

Explanation:

Step1: Recall volume formula

The volume formula for a cylinder is $V = \pi r^{2}h$, where $V$ is volume, $r$ is radius and $h$ is height.

Step2: Substitute given values

We know $V = 500\ cm^{3}$ and $h=10\ cm$. Substituting into the formula gives $500=\pi r^{2}\times10$.

Step3: Solve for $r^{2}$

First, divide both sides of the equation by $10\pi$: $r^{2}=\frac{500}{10\pi}=\frac{50}{\pi}$.

Step4: Solve for $r$

Take the square - root of both sides: $r=\sqrt{\frac{50}{\pi}}$. Using $\pi\approx3.14$, we have $r=\sqrt{\frac{50}{3.14}}\approx\sqrt{15.92}\approx 4\ cm$.

Answer:

A. 4 cm