Question

A soft drink company wants to increase the volume of the cylindrical can they sell soft drinks in by 25%. The company wants to keep the 5-inch height of the can the same. The radius of the can is currently 2.5 inches. Approximately how much should the radius of the can be increased

Answer 1

Answer:

https://slideplayer.com/slide/14286858/ copy paste the link it has a bunch of the answers but sadly no work on it.

Step-by-step explanation:

Answer 2

Answer:

The radius should be increased by 0.295 inches.

Step-by-step explanation:

Volume of a cylinder:

In a cylinder, in which the base has radius $r$, and the height is $h$, the volume is given by:

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

In this question:

5 inch height, radius of 2.5 inches. So the volume is given by:

$V = \pi (2.5)^2(5) = 31.25\pi$

We want to increase the volume by 25%.

So, the new volume is given by:

$1.25*31.25\pi = 39.0625\pi$

With this volume, keeping the height, the radius should be of:

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

$39.0625\pi = 5\pi r^{2}$

$r^{2} = \frac{39.0625}{5}$

$r^{2} = 7.8125$

$r = \sqrt{7.8125}$

$r = 2.795$

The radius should be of 2.795 inches, which is an increase of 2.795 - 2.5 = 0.295 inches.