Question

What’s the height of the can?

Answer 1

5 inches

Explanation:

The formula to find the surface area of a cylinder is A = 2πrh + 2πr²

Since we need the height we will need to solve for h

• First we can subtract 2πr² from both sides to get A - 2πr² = 2πrh
• Then we can divide both sides by 2πr to get
  `h=(A-2\pi r^(2) )/(2\pi r)`

Now we can plug in our known values and solve for h

• Here we were given the diameter, d, however this formula is in terms of the radius, r.
• The diameter is equivalent to double the radius, d = 2r
• Therefore the radius is equivalent to half the diameter,
  `r=(1)/(2) d`
• Plugging in d to solve for r we get
  `r=(1)/(2)(2)` which simplifies to r = 1

The two variables for this equation we have no obtained, A = 12π and r = 1, so we can plug them into our equation to solve for the height

• 
  `h=(12\pi -2\pi (1)^(2) )/(2\pi (1))=h=(12\pi -2\pi )/(2\pi )=(10\pi )/(2\pi ) =5`
• The height is 5 inches