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What’s the height of the can?

What’s the height of the can?-example-1
User Bwbecker
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1 Answer

3 votes

Answer:

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
User Sestocker
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