Question

A cylindrical can of seltzer water has a height of 5 inches and a radius of 1 inch, as shown below. What is the longest straw that can fit completely inside of the can of seltzer water?

Answer 1

Given:

Height of cylinder = 5 inches

Radius = 1 inch

Consider that a straw can be inserted from one corner of the cylindrical can to fit completely inside of the can. When this happens, you can take the straw to be the hypotenuse of a right triangle.

We have the image below:

The blue line can be said to be the straw.

To find the length of this, use pythagoras theorem:

`c^2=a^2+b^2`

We are to take the diameter as the base.

diameter = 2 x radius

= 2 x 1 = 2 ft

Thus, we have:

`\begin{gathered} c^2=5^2+2^2 \\ \\ ^{} \end{gathered}`

Solve for c:

`\begin{gathered} c^2=25+4 \\ \\ c^2=29 \\ \\ \sqrt[]{c^2}=\sqrt[]{29} \\ \\ c=5.39\text{ ft} \end{gathered}`

Therefore, the length of the longest straw that can completely fit inside of this cylindrical can is approximately 5.39 ft

ANSWER:

5.39 ft