Geometry Word Problem!

Question

A cylindrical carton of raisins with radius 4 cm is 25 cm tall. If all surfaces EXCEPT the top are made of cardboard, how much cardboard is used to make the raising carton? Round your answer to the nearest square centimeter --- Please give me an explanation not just an answer

Answer 1

Thankfully, the problem gives us the information crucial to solving this problem!

First, recognize which parts of the cylinder you need to find the surface area of in order to complete the problem.  The problem states for "all surfaces EXCEPT the top."  This is our clue.  With that, we know we are finding the surface area of the lateral surface of the cylinder (the formula for that is A =  2πrh, with r = radius, and h = height), and we need to find the area of ONE of the circles that make up that entire cylinder (the formula for area of a circle is A = πr²).  Add those two areas together, and, viola, you have the area of the cylinder the problem asks for.

 

Now, let's set up our equations!  What do we know?

 

r = 4cm

h = 25cm

 

Area of cylinder = 2*π*4*25 = 200π

Area of a circle = π*4² = 16π

 

Now, we add our two areas together!

 

200π + 16π = 216π, which is approximately equal to 679cm²!

 

The total amount of materials is approximately 679 cm².  Hope that helps!

 

Edit:  I believe I used the wrong terminology.  I used "outside of the cylinder" when I really meant was the "lateral surface" of the cylinder.  Basically, this refers to the portion of the cylinder that is neither of the circles on the top/bottom of the cylinder.