Question

A nut company is determining how to package their new type of party mix. The marketing department is experimenting with different-sized cans for the party mix packaging. The designers use the equation r=Vhπ⎯⎯⎯⎯⎯⎯√r=Vhπ to determine the radius of the can for a certain height hh and volume VV. The company decides they want the can to have a volume of 1280πcm31280π⁢cm3. Find the radius of the can if the height is 16cm16⁢cm. Keep your answers in simplified radical form.

Answer 1

Answer:

The radius of the can, in centimeters, is of $4\sqrt{5}$

Step-by-step explanation:

Radius of the can:

The radius of the can is given by:

$r^2 = \frac{V}{h\pi}$

In which V is the volume and h is the height.

In this question:

$V = 1280\pi, h = 16$

Thus

$r^2 = \frac{V}{h\pi}$

$r^2 = \frac{1280\pi}{16\pi}$

$r^2 = 80$

$r = \sqrt{80}$

$r = \sqrt{5*16}$

$r = \sqrt{5}\sqrt{16}$

$r = 4\sqrt{5}$

The radius of the can, in centimeters, is of $4\sqrt{5}$